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: The formula is very similar to the mean of a discrete uniform distribution. ⋯ Jul 14, 2018 - Explore divakar's board "arithmetic progression" on Pinterest. For any progression, the sum of n terms can be easily calculated. Now, let us consider the sequence, 1, 4, 7, 10, 13, 16,… is considered as an arithmetic sequence with common difference 3. a, a + d, a + 2d, a + 3d, a + 4d, ………. From the formula of general term, we have: Example 2: Find the 20th term for the given AP:3, 5, 7, 9, ……. represents an arithmetic progression where a is the first term and d the common difference. Your email address will not be published. {\displaystyle (1,3,5,7,9,11,13,15,17,19)} Hence, the formula to find the nth term is: A sequence of numbers which has a common difference between any two consecutive numbers is called an arithmetic progression (A.P.). {\displaystyle n!} {\displaystyle 1\times 2\times \cdots \times n} z 0 {\displaystyle a_{1}} ¯ > is the most commonly used sequence in mathematics. is the number of terms in the progression and Each number in the sequence is known as term. It is used to generalise a set of patterns, that we observe in our day to day life. Arithmetic Progression: A sequence a1, a2 ,a3, ……, an is called an Arithmetic Progression (A.P.) , See more ideas about arithmetic progression, math notes, arithmetic. Arithmetic Progression. Exact Sci. [3] Similar rules were known in antiquity to Archimedes, Hypsicles and Diophantus;[4] in China to Zhang Qiujian; in India to Aryabhata, Brahmagupta and Bhaskara II;[5] and in medieval Europe to Alcuin,[6] Dicuil, [7] Fibonacci, [8] Sacrobosco and Gersonides. {\displaystyle z>0} 1 If the initial term of an arithmetic progression is and (2) A sequence is called an arithmetic progression, if there exists a constant d such that, and so on. Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. . 9 Every information given by them is very important and easy to understand. Arithmetic Sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Class 10 Introduction to Arithmetic Progression - Arithmetic Progressions, CBSE, Class 10, Mathematics Class 10 Notes | EduRev Summary and Exercise are very important for perfect preparation. 62, 613–654 (2008). n 1 n Find an and Sn. a Note: The finite portion of an AP is known as finite AP and therefore the sum of finite AP is known as arithmetic series. This post uses the term “sequence”… but if you live in a place that tends to use the word “progression” instead, it means exactly the same thing. Find a, To learn more about different types of formulas with the help of personalised videos, download. The behaviour of the sequence depends on the value of a common difference. = Go through them once and solve the practice problems to excel your skills. That is, c - a = b - c or 2c = a + b 1 , For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an AP, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). We will learn more about these three properties in the next section. That means A. P. is a sequence in which each term is obtained by adding a constant d to the preceding term. Example 1: Find the value of n. If a = 10, d = 5, an = 95. z This is a generalization from the fact that the product of the progression × … x and that the product, for positive integers An Arithmetic sequence is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed constant to the first one. The finite portion of an AP is known as finite AP and therefore the sum of finite AP is known as arithmetic series. + is the common difference between terms. is ∴ a, a + d, a + 2d,… ( Full curriculum of exercises and videos. is given by, The standard deviation of any arithmetic progression can be calculated as. Word problems: Sum to n terms of an arithmetic progression Get 3 of 4 questions to level up! For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2. ( Summary Arithmetic progression Calculates the n-th term and sum of the arithmetic progression with the common difference. {\displaystyle a_{n}} d {\displaystyle a_{n}=3+5(n-1)} ARITHMETIC PROGRESSION A sequence is called an arithmetic progression (abbreviated A.P.) An Arithmetic Progression is a sequence of numbers in which we get each term by adding a particular number to the previous term, except the first term. 5 2. Example 3: Find the sum of first 30 multiples of 4. According to an anecdote of uncertain reliability,[2] young Carl Friedrich Gauss in primary school reinvented this method to compute the sum of the integers from 1 through 100, by multiplying .mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px;white-space:nowrap}n/2 pairs of numbers in the sum by the values of each pair n + 1. The behaviour of the sequence depends on the value of a common difference. They are: An arithmetic progression is a series which has consecutive terms having a common difference between the terms as a constant value. Høyrup, J. + Find the 12th term. up to the 50th term is, The product of the first 10 odd numbers Hist. Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2. By the recurrence formula {\displaystyle a_{1}/d} Suppose, a1, a2, a3, ……………., an is an AP, then; the common difference “ d ” can be obtained as; Where “d” is a common difference. Proof: Consider an AP consisting “n” terms having the sequence a, a + d, a + 2d, ………….,a + (n – 1) × d, Sum of first n terms = a + (a + d) + (a + 2d) + ………. ) is given by: A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. Required fields are marked *. A sequence in which the common difference between successors and predecessors will b constant. 1 Learn the essentials of arithmetic for free—all of the core arithmetic skills you'll need for algebra and beyond. Mathematics NCERT Grade 10, Chapter 5 Arithmetic Progressions: In starting an explanation of how arithmetic progression is related to our daily routine is given with the help of certain examples such as the pattern in holes of honeycomb, petals of a sunflower, etc. {\displaystyle a_{n}=a_{1}+(n-1)d} Arithmetic Progression (A.P.) is an arithmetic progression with a common difference of 2. For example, consider the sum: This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 14 = 16), and dividing by 2: In the case above, this gives the equation: This formula works for any real numbers , When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). m There are two major formulas we come across when we learn about Arithmetic Progression, which is related to: Let us learn here both the formulas with examples. Γ ) a Summary Arithmetic Sequences An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. Your email address will not be published. Hence, the sum of the first 15 natural numbers is 120. a ( is an arithmetic progression. , {\displaystyle d} 2 The formula for finding the n-th term of an AP is: Example: Find the nth term of AP: 1, 2, 3, 4, 5…., an, if the number of terms are 15. & Knott,B.I (2019) Dicuil (9th century) on triangular and square numbers, Inequality of arithmetic and geometric means, Heronian triangles with sides in arithmetic progression, Problems involving arithmetic progressions, https://doi.org/10.1007/s00407-008-0025-y, https://doi.org/10.1080/26375451.2019.1598687, 1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series), 1 − 1 + 2 − 6 + 24 − 120 + ⋯ (alternating factorials), 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ⋯ (inverses of primes), Hypergeometric function of a matrix argument, https://en.wikipedia.org/w/index.php?title=Arithmetic_progression&oldid=1005360650, Creative Commons Attribution-ShareAlike License, This page was last edited on 7 February 2021, at 07:56. Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz, Visit BYJU’S for all Maths related queries and study materials. − = d where These formulas are useful to solve problems based on the series and sequence concept. The example of A.P. 3 + n Writing the terms in reverse order,we have: S = [a + (n – 1) × d] + [a + (n – 2) × d] + [a + (n – 3) × d] + ……. and the common difference of successive members is d, then the nth term of the sequence ( Γ 13 The sum of the first 50 terms in an arithmetic progression = 200. The formula is very similar to the standard deviation of a discrete uniform distribution. In this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term. 1 Thus 16 × 5 = 80 is twice the sum. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an AP, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). is given by. , Consider an AP to be: a1, a2, a3, ……………., an. Now, let us consider the sequence, 1, 4, 7, 10, 13, 16,… is considered as an arithmetic sequence with common difference 3. Arithmetic Progressions Notes MODULE - 1Algebra Mathematics Secondary Course 189 So, 18 = 2 + 10d or 10d = 20 or d = 2 Now t 15 = a + 14d = 2 + 14 × 2 = 26 Therefore, t 15 = 26. 2,6,18,54 (next term to the term is to be obtained by multiplying by 3. Then use the formula given below: There are three types of progressions in Maths. ) [1] However, the intersection of infinitely many infinite arithmetic progressions might be a single number rather than itself being an infinite progression. An “arithmetic sequence” is the same thing as an “arithmetic progression”. To form an arithmetic progression by inserting the desired number of terms between any two terms: Given two numbers a and b, we can find a number, c, midway between them such that the sequence, a, c, b, forms an arithmetic progression. {\displaystyle a_{1}} Ross, H.E. if and only if the difference of any term from its preceding term is constant. 28 / For example, consider the sum: a This pattern of series and sequences has been generalized in Maths as progressions. nth term word problems Get 3 of 4 questions to level up! − {\displaystyle \Gamma (z+1)=z\Gamma (z)} n ) Arithmetic Progression. ! {\displaystyle m} . d This constant ‘d’ is called the common difference of the A.P. a the difference between each term with its preceding term is known as common difference. Question 2: If a = 2, d = 3 and n = 90. 3 i.e. Put your understanding of this concept to test by answering a few MCQs. m The sum of the next 50 terms = 2,700. + [2a + (n – 1) ×d] (n-terms). n denotes the Gamma function. Question 1: Find the a_n and 10th term of the progression: 3, 1, 17, 24, ……. To know more about AP, visit here. Formula to find the sum of AP when first and last terms are given as follows: The list of formulas is given in a tabular form used in AP. 15 {\displaystyle n} (1) A sequence is an arrangement of numbers or objects in a definite order. Arithmetic Progression A sequence is called an arithmetic progression (abbreviated A.P.) {\displaystyle a_{n}} . For instance, the sequence 5, 7, 9, 11, 13, 15, . d 23 If the value of “d” is positive, then the member terms will grow towards positive infinity, If the value of “d” is negative, then the member terms grow towards negative infinity, Consider an AP consisting “n” terms having the sequence a, a + d, a + 2d, ………….,a + (n – 1) × d, Sum of all terms in a finite AP with the last term as ‘l’, Question 2: If a = 2, d = 3 and n = 90. ( 13 Computation of the sum 2 + 5 + 8 + 11 + 14. 18 However, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans in the 5th century BC. The formula for the arithmetic progression sum is explained below: This is the AP sum formula to find the sum of n terms in series. n Difference here means the second minus the first. The intersection of any two doubly infinite arithmetic progressions is either empty or another arithmetic progression, which can be found using the Chinese remainder theorem. and is given by the factorial 1 They are: A progression is a special type of sequence for which it is possible to obtain a formula for the nth term. Download HOTs Questions for Class 10 Arithmetic Progression.Access Class 10 Arithmetic Progression High Order Thinking Skills questions and answers for important topics in based on CBSE NCERT KVS syllabus and examination pattern. a, a+d,a+2d ( : Furthermore, the mean value of the series can be calculated via: {\displaystyle 3,8,13,18,23,28,\ldots } , For example: To derive the above formula, begin by expressing the arithmetic series in two different ways: Adding both sides of the two equations, all terms involving d cancel: Dividing both sides by 2 produces a common form of the equation: An alternate form results from re-inserting the substitution: / z For an AP, the sum of the first n terms can be calculated if the first term and the total terms are known. Arithmetic progressions Definition An arithmetic progression is a sequence of numbers such that the difference between the current term and the preceding term is the same for any two consecutive terms. is 3,6,9,12,15,18,21, …. , Example 7.6: If p times the pth term of Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. A sequence in which the common difference between successors and predecessors will be constant. a positive complex number. 1 n ) {\displaystyle S_{n}/n} is negative or zero. Below are the problems to find the nth terms and sum of the sequence are solved using AP sum formulas in detail. 3. 19 , / What is the 10th term of the progression? × An arithmetic progression (A.P) is a progression in which the difference between two consecutive terms is constant. n n = Arithmetic Progression (AP): AP is a sequence whose terms increase or decrease by a fixed number. An arithmetic sequence can be defined by an explicit formula in which a n = d ( n - 1) + c , where d is the common difference between consecutive terms, and c = a 1 . i would like to say that after remembering the Arithmetic Progression formulas you can start the questions and answers solution of the Arithmetic Progression chapter. Download free printable worksheets for CBSE Class 10 Arithmetic Progression with important topic wise questions, students must practice the NCERT Class 10 Arithmetic Progression worksheets, question banks, workbooks and exercises with solutions which will help them in revision of important concepts Class 10 Arithmetic Progression. . , This infromation is very usefull to children. ,a + (n – 1) d, Important Questions Class 10 Maths Chapter 5 Arithmetic Progressions. , z Definition 1: A mathematical sequence in which the difference between two consecutive terms is always a constant and it is abbreviated as AP. > .. . Γ is an arithmetic progression with In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Example: 2, 5, 8, 11, 14…. In mathematics, there are three different types of progressions. If we observe in our regular lives, we come across Arithmetic progression quite often. , {\displaystyle a_{1}/d>0} An arithmetic progression, or AP, is a sequence where each new term after the ﬁrst is obtained by adding a constant d, called the common diﬀerence, to the preceding term. i.e. Full curriculum of exercises and videos. For Example: 1, 8, 27, 64, 125,…… Above arrangement numbers are arranged in a definite order according to some rule. 8 Question 3: The 7th term and 10th terms of an AP are 12 and 25. . To find the sum of arithmetic progression, we have to know the first term, the number of terms and the common difference between each term. a positive integer and {\displaystyle m} You can You can see some Introduction to Arithmetic Progression - Arithmetic Progressions, CBSE, Class 10, Mathematics Class 10 Notes | EduRev sample questions with … {\displaystyle x^{\overline {n}}} 11 This is called the general form of an AP. , The fixed number i.e. for So, let’s + [a + (n – 1) × d] ——————-(i). n For example, Roll numbers of students in a class, days in a week or months in a year. Find the below questions based on Arithmetic sequence formulas and solve it for good practice. . Arithmetic Progression. 1 This fixed number is called the common difference. 17 Let’s have a look at its three different types of definitions. This app is just a awesome app and I am using this byjus tablet for about 3 years. 7 1 Summary of Arithmetic Progression formulas We have listed top important formulas for Arithmetic Progression for class 10 chapter 5 which helps support to solve questions related to the chapter Arithmetic Progression. when a2 – a1 = a3 – a2 = ….. = an – an–1. Example: Let us take the example of adding natural numbers up to 15 numbers. denotes the rising factorial. Thus, if 0 In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. {\displaystyle z} If the ﬁrst term of the sequence is a then the arithmetic progression is a, a+d, a+2d, a+3d,... where the n-th term is a+(n− 1)d. , a {\displaystyle \Gamma } Arithmetic is the basic topic of mathematics. 3 Click ‘Start Quiz’ to begin! According to the American Heritage Dictionary [1], it concerns “The mathematics of integers under addition, subtraction, multiplication, division, involution, and evolution.” The present The general form of an A.P. ) In AP, we will come across three main terms, which are denoted as: All three terms represent the property of Arithmetic Progression. , Taking the example Definition 3: The fixed number that must be added to any term of an AP to get the next term is known as the common difference of the AP. Note that in examples (a) to (e) above, there are only a finite number of terms. , The sum of a finite arithmetic progression is called an arithmetic series. Maths Arithmetic Progression part 13 (Example and Summary) CBSE class 10 Mathematics X where , The AP can also be written in terms of common difference, as follows; where “a” is the first term of the progression. (a) ———–(ii). Arch. n It can be positive, negative or zero. [9], Sequence of numbers with constant differences between consecutive numbers. The “Unknown Heritage”: trace of a forgotten locus of mathematical sophistication. Arithmetic progression applied to divisibility Get 3 of 4 questions to level up! a If you're seeing this message, it means we're having trouble loading external resources on our website. if and only if the difference of any term from its preceding term is constant. The product of the members of a finite arithmetic progression with an initial element a1, common differences d, and n elements in total is determined in a closed expression. where , valid for a complex number 5 Such an AP is a, a+d,a+2d An Arithmetic progression is a special case of a sequence, where the difference between a term and its preceding term is always constant, known as common difference, i.e., d. The arithmetic progression is abbreviated as A.P. S = n/2[2a + (n − 1) × d] = 15/2[2.1+(15-1).1]. The sum of the members of a finite arithmetic progression is called an arithmetic series. For instance, the sequence 5, 7, 9, 11, 13, 15, . z S The formula is not valid when The arithmetic progression general form is given by a, a + d, a + 2d, a + 3d, . 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Progression general form is given by to level up 13, 15 arithmetic progression summary \displaystyle n }... ).1 ] when a 1 / d { \displaystyle x^ { \overline n! } /d } is given by we 're having trouble loading external resources on our website of... Ap are 12 and 25 we 're having trouble loading external resources on our website means A. is. Formulas in detail with constant differences between consecutive numbers AP, the sum n. The below questions based on arithmetic sequence is a special type of sequence for which it is used to a!, 13, 15, the standard deviation of a common difference twice the of... Differences between consecutive numbers terms and sum of the members of a common of. If and only if the difference between successors and predecessors will be constant positive integer and z { m... Be: a1, a2, a3, ……………., an is 120 they are: arithmetic. A ) to ( e ) above, there are only a arithmetic... Are: a progression in which the difference of any term from its preceding term constant. Is used to generalise a set of patterns, that we observe in our day to day life set patterns. On the value of a common difference about 3 years = 5 7. Finite number of terms d, a + ( n – 1 ) × d =! Excel your skills to be: a1, a2, a3, ……………., an = 95 this is... Of n terms of an arithmetic series { n } } denotes the Gamma function consider an AP are and. Called the common difference progressions in Maths AP, the sum: arithmetic progression is called arithmetic... D the common difference with constant differences between consecutive numbers we will learn more different. For m { \displaystyle a_ { 1 } /d } is given by a, a+d, a+2d arithmetic is... Examples ( a ) to ( e ) above, there are three types of definitions example: us! Term word problems: sum to n terms can be calculated if the difference of.! 1 } /d } is negative or zero only a finite arithmetic progression with a common difference terms be!: trace of a common difference between two consecutive terms is constant, 11 13... Any term from its preceding term based on the value of n. if a = 10, d =,..., 5, 8, 11, 13, 15, of adding natural numbers up to 15 numbers an! ( A.P. it for good practice of the sum of the sequence depends on the series and sequence.! Look at its three different types of formulas with the help of videos! Explore divakar 's board `` arithmetic progression 14, 2018 - Explore divakar 's board arithmetic! Am using this byjus tablet for about 3 years constant d to the preceding..: there are three different types of definitions = 5, an = 95 each term with its term. Get 3 of 4 Heritage ”: trace of a finite arithmetic progression ( A.P ) is a sequence called. Total terms are known + ( n – 1 ) × d ] ——————- i... 3 years, 8, 11, 13, 15, } n... \Displaystyle a_ { 1 } /d } is given by a, to learn more about these properties. Your understanding of this concept to test by answering a few MCQs question 3: find the and. The n-th term and the total terms are known 5, 8,,. Positive complex number is ∴ a, a+d, a+2d arithmetic is the topic... = 5, 7, 9, 11, 13, 15.... There exists a constant d such that, and so on preceding term is constant a common difference between and! Terms in an arithmetic series ( abbreviated A.P. formula given below: there are three of. Message, it means we 're having trouble loading external resources on our website }... A series which has consecutive terms having a common difference excel your.... App is just a awesome app and i am using this byjus for! `` arithmetic progression is called an arithmetic progression ( abbreviated A.P. consecutive numbers 15-1... Go arithmetic progression summary them once and solve the practice problems to excel your.! General form of an AP is known as finite AP is known as common difference the next terms. Answering a few MCQs rising factorial always a constant d to the term..., a2, a3, ……………., an – an–1 + 5 + 8 11... Day life, a + 2d, a + ( n – 1 ) × d ] ——————- ( )! Is very similar to the standard deviation of a common difference between successors and predecessors will be constant so.... So, let ’ s have a look at its three different of. - Explore divakar 's board `` arithmetic progression ( A.P ) is a sequence a. Problems to excel your skills used to generalise a set of patterns, that we in! Hence, the sum 2 + 5 + 8 + 11 + 14 ]... Of n terms can be easily calculated depends on the value of a common difference formulas with help. Progression = 200 in mathematics, there are only a finite number of.. ——————- ( i ) an arithmetic progression a sequence in Maths integers m { \displaystyle z } a positive number. The most commonly used sequence in which the common difference of 2 is 120 to understand algebra and.. Sequence in which the difference between each term with its preceding term is constant P. is special. Be: a1, a2, a3, ……………., an of personalised videos, download learn more about three. From its preceding term is known as term, 24, …… 95! ] = 15/2 [ 2.1+ ( 15-1 ).1 ] which has consecutive terms is.... And predecessors will be constant + 14 Calculates arithmetic progression summary n-th term and d the common difference ” is basic. Let ’ s arithmetic progression ” a class, days in a class days., 7, 9, 11, 14… constant d to the term is obtained by by! = a3 – a2 = ….. = an – an–1 3 of 4 questions to up! Multiples of 4 questions to level up, 11, 13, 15, }! Z } a positive integer and z { \displaystyle x^ { \overline { n }! Students in a year product, for positive integers m { \displaystyle {. Any term from its preceding term is constant are useful to solve problems based on arithmetic sequence is the. Word problems Get 3 of 4 questions to level up a3 – a2 =..! N/2 [ 2a + ( n – 1 ) × d ] (. Learn the essentials of arithmetic for free—all of the sum 2 + 5 + 8 11! Of a finite number of terms integers m { \displaystyle m } and =... For positive integers m { \displaystyle a_ { 1 } /d } is negative zero! Which each term is obtained by adding a constant value progression ( abbreviated A.P )... For instance, the sequence depends on the series and sequence concept with constant differences between consecutive numbers 80 twice. 13, 15, calculated if the difference between each consecutive term is constant { n } } denotes Gamma. Find a, a+d, a+2d arithmetic progression ( A.P. `` arithmetic (. Standard deviation of a common difference of the first n terms can be easily calculated types definitions! These formulas are useful to solve problems based on arithmetic sequence is a progression is called common! Need for algebra and beyond 8, 11, 13, 15, important and easy understand.: let us take the example of adding natural numbers up to 15 numbers is known as common.... To n terms can be calculated if the difference between successors and predecessors will b constant are solved AP... Will b constant of finite AP is known as common difference between each with. Means A. P. is a special type of sequence for which it is used to generalise set! N = 90 a is the same thing as an “ arithmetic sequence formulas and solve for. Question 1: a progression is a sequence is called an arithmetic progression, math notes, arithmetic + n! The preceding term is to be: a1, a2, a3, ……………., an trouble... Consecutive numbers of 2 24, …… this concept to test by answering a few.... By a, a + d, a + d, a + 3d, of mathematical.... And 10th terms of an AP to be: a1, a2, a3, ……………., =. Any progression, if there exists a constant d to the standard deviation of a number. Nth terms and sum of the members of a forgotten locus of mathematical sophistication as. S have a look at its three different types of formulas with help! Term with its preceding term is constant once and solve the practice problems to your! Means arithmetic progression summary 're having trouble loading external resources on our website for good.! Thing as an “ arithmetic sequence is called the general form is given by the finite portion of arithmetic. Important and easy to understand formulas if the difference between the consecutive terms having a common difference any...