Ex 9.2, 8 - If sum of n terms of an A.P. is (pn + qn2), find common difference. - Arithmetic Progression (AP): Calculation based/Proofs

Ex 9.2, 8 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.2, 8 - Chapter 9 Class 11 Sequences and Series - Part 3

This video is only available for Teachoo black users

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question8 If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference. Let a1, a2, an be the given A.P Given, Sum of n terms = (pn + qn2) Sn = (pn + qn2) Putting n = 1 in (1) S1 = (p 1 + q 12) = p + q 1 = p + q Sum of first 1 terms = First term First term = a1 = S1 = p + q Sn = (pn + qn2) (1) Putting n = 2 in (1) S2 = (p 2 + q 22) = 2p + q 4 = 2p + 4q Sum of first two terms = First term + Second term S2 = a1 + a2 S2 a1 = a2 a2 = S2 a1 Putting a1 = p + q , S2 = 2p + 4q a2 = (2p + 4q) (p + q) = 2p + 4q p q = p + 3q Thus, a1 = p + q & a2 = p + 3q Common difference = Second term First term = a2 a1 = (p + 3q) (p + q) = 3q q = 2q

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.