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 = 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.