Question 2 - Arithmetic Progression (AP): Calculation based/Proofs - Chapter 8 Class 11 Sequences and Series

Last updated at Dec. 16, 2024 by

Example 5 - If sum of n terms of AP is nP + 1/2n(n-1)Q - Arithmetic Progression (AP): Calculation based/Proofs

Example 5 - Chapter 9 Class 11 Sequences and Series - Part 2
Example 5 - Chapter 9 Class 11 Sequences and Series - Part 3

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Question 2, If the sum of n terms of an A.P. is nP + 1/2n(n 1)Q , where P and Q are constants, find the common difference. Let a1, a2, an be the given A.P Given, Sum of n terms = nP + 1/2 n (n 1) Q Sn = nP + 1/2 n (n 1) Q Putting n = 1 in (1) S1 = 1 P + 1/2 1 (1 1)Q S1 = P + 1/2(0) S1 = P But sum of first 1 terms will be the first term a1 = S1 = P Sn = nP + 1/2 n (n 1) Q (1) Putting n = 2 in (1) S2 = 2P + 1/2 2(2 1)Q S2 = 2P + 1/2 2 1 Q S2 = 2P + Q Sum of first two terms = First term + Second term S2 = a1 + a2 S2 a1 = a2 a2 = S2 a1 Putting a1 = P , S2 = 2P + Q a2 = 2P + Q P = 2P P + Q = P + Q Thus, a2 = P + Q Common difference (d) = a2 a1 = (P + Q) P = Q Hence, common difference of the given A.P. is Q

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo