In an AP, the first term is 22, nth term is -11 and sum of first n ter

1.	In an AP, the first term is 22, nth term is -11 and sum of first n terms is 66. Find n and hence find the common difference.
Answer» Let n be the total number of terms and d be the common difference. Given: first term = a = 22 nth term = -11 Sum of all terms = S_n = 66 S_n = n/2[a + l] 66 = n/2[22 + (-11)] n = 12 There are 12 terms in the AP. Since nth term is -11, so a_n = a + (n – 1)d -11 = 22 + (12-1)d d = -3 Therefore, Common difference is -3 and the number of terms are 12.

In an AP, the first term is 22, nth term is -11 and sum of first n terms is 66. Find n and hence find the common difference.

Answer»

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

Given:

first term = a = 22

nth term = -11

Sum of all terms = S_n = 66

S_n = n/2[a + l]

66 = n/2[22 + (-11)]

n = 12

There are 12 terms in the AP.

Since nth term is -11, so

a_n = a + (n – 1)d

-11 = 22 + (12-1)d

d = -3

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