Given,
The first term of the A.P (a) = 22
The nth term of the A.P (l) = -11
And, sum of all the terms Sn = 66
Let the common difference of the A.P. be d.
So, finding the number of terms by
66 = (\(\frac{n}{2}\))[22 + (−11)]
66 = (\(\frac{n}{2}\))[22 − 11]
(66)(2) = n(11)
6 × 2 = n
n = 12
Now, for finding d
We know that, l = a + (n – 1)d
– 11 = 22 + (12 – 1)d
-11 = 22 + 11d
11d = – 33
d = – 3
Hence, the number of terms is n = 12 and the common difference d = -3