Page 1 Arithmetic Progressions Page 2 Arithmetic Progressions a - rst number of an A. P . d - common dierence of an A. P . a n - term of an A. P . n - number of terms A sequence of numbers in which each diers from the preceding one by a constant quantity (common dierence). If the sequence is increasing, common dierence is positive; if it is decreasing, common dierence is negative. 15, 10, 5, 0, -5 This formula is used to calculate sum of rst n terms. It can also be used to nd a or d when rest of the information is given The same formula is used to calculate number of terms when sum (s n ) and a & d are given means it adds all the numbers starting from the ?rst to n th [average of rst (a) & last term (l)] x n n s n = a + l 2 s n = 2a + (n - 1) d n 2 3 4 5 1 a n = a + (n - 1) d This formula is used to calculate : The value of any term in A. P . when a, n, d is given Similarly, it can also be used to calculate d or a when other imformation like a n , n is given One can also use this to calculate numbers of term of an A. P . + 1 n = a n - a d a n - last term Where a - rst term 1 2 3 Some important points : s 1 = a 1 1 s n - s n - 1 = a n 2 a n - a m = (n - m) d 3 a n - a n - 1 = d 4 ARITHMETIC PROGRESSIONS 12 Arithmetic Progressions Page 3 Arithmetic Progressions a - rst number of an A. P . d - common dierence of an A. P . a n - term of an A. P . n - number of terms A sequence of numbers in which each diers from the preceding one by a constant quantity (common dierence). If the sequence is increasing, common dierence is positive; if it is decreasing, common dierence is negative. 15, 10, 5, 0, -5 This formula is used to calculate sum of rst n terms. It can also be used to nd a or d when rest of the information is given The same formula is used to calculate number of terms when sum (s n ) and a & d are given means it adds all the numbers starting from the ?rst to n th [average of rst (a) & last term (l)] x n n s n = a + l 2 s n = 2a + (n - 1) d n 2 3 4 5 1 a n = a + (n - 1) d This formula is used to calculate : The value of any term in A. P . when a, n, d is given Similarly, it can also be used to calculate d or a when other imformation like a n , n is given One can also use this to calculate numbers of term of an A. P . + 1 n = a n - a d a n - last term Where a - rst term 1 2 3 Some important points : s 1 = a 1 1 s n - s n - 1 = a n 2 a n - a m = (n - m) d 3 a n - a n - 1 = d 4 ARITHMETIC PROGRESSIONS 12 Arithmetic Progressions Tricks to remember formulae and tips to solve dicult questions. Introduction of Arithmetic Progressions Problem solving based on a n . How to avoid mistakes in Arithmetic Progressions Scan the QR Codes to watch our free videos For determining the A.P . or to nd next terms of A.P . always try to nd ‘a’ and ‘ d’ . There are two formulas in AP and each of them is assembled of 4 variables. We use these formulas to nd one missing variable when the information about the other three are given. PLEASE KEEP IN MIND If it talks about, price/ rent/ fare on a particular time (day, month, hour) then it’s a question of a n . When sum of two terms or addition two A.P . ’s is given, then write them in the from of ‘a+nd ’ and solve the two formed linear equations simultaneously. ? ? ? When relation between any two terms of a sequence is given in whatever way try to write them in the form of ‘a+nd’ and then solve for ‘n’ , ‘a’ or ‘ d’ . ? To know the number of terms(n), rst term (a), common dierence (d), we can use any of the two formulas (a n & S n ). The only thing is to recogise whether information about the sum or term of A.P . is given. ? There are questions where we have to nd multiple of a number, divisible by a number, when divided by this number leaves remainder, in all these types of questions the common dierence is that number only. ? ? ? To recognise whether the sequence of a number is forming an A.P . or not, we should check for the common dierence that should be equal. In word problems, when it talks about total rent/ fare/ amount or something like that then it’s a question on S n . ? ARITHMETIC PROGRESSIONS 13Read More

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