One of the most important question of arithmetic progression chapter as it was already asked in previous year paper of 2008 in which we have to find the common difference and the number of terms, if the first term is 22, nth term is -11 and the sum of first n terms is 66 of an AP.

Book RS Aggarwal, Class 10, chapter 5C, question no 25.

Let n be the total number of terms and d be the common difference.

Given:

First term =a=22

nth term or last term l=−11

Sum of all terms =Sn=66

Sn=n/2[a+l]

66=n/2[22+(−11)]

n=12

There are 12 terms in the AP.

Since nth term is −11, so

an=a+(n−1)d

−11=22+(12−1)d

d=−3

Therefore, Common difference is −3 and the number of terms are 12.