In an A.P., the first term is 22, nth term is -11 and the sum to first n terms is 66. Find n and d, the common difference.
Given, First term, a = 22
nth term, an= -11 = l
and sum of n terms, Sn= 66
We know sum of n terms, Sn= [a + l]
66 = [22 – 11]
66 * 2 = n * 11
n = = 12
we know, an= a + (n – 1) d
-11 = 22 + (12 – 1) d
-11 – 22 = 11d
-33 = 11d
d = -3
Hence, number of terms, n = 12 and common difference, d = -3