One of the most important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2006 in which we have been asked to find the nth term and the 25th term, if the sum of the first n terms of an AP is (3n^2/2 + 5n/2)
Book- RS Aggarwal, Class 10, chapter 5C, question no 6(ii).
Given Sn=3n2−n
Then Sn−1=3[3(n−1)]2−(n−1)
an=Sn−Sn−1
⇒an=[3n2−n]−[3(n−1)2−(n−1)]
=3[n2−(n−1)2]−n+n−1
=3(n2−n2+2n−1)−1=3(2n−1)−1=6n−4
Then, a25=6×25−4=150−4=146