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.

LetÂ nÂ be the total number of terms andÂ dÂ be the common difference.

Given:

First termÂ =a=22

nth term or last termÂ l=âˆ’11

Sum of all termsÂ =Snâ€‹=66

Snâ€‹=n/2[a+l]

66=n/2[22+(âˆ’11)]

n=12

There areÂ 12Â terms in the AP.

Since nth term isÂ âˆ’11, so

anâ€‹=a+(nâˆ’1)d

âˆ’11=22+(12âˆ’1)d

d=âˆ’3

Therefore, Common difference isÂ âˆ’3Â and the number of terms areÂ 12.