# 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.

Here, first term = a = 22

Let the Common difference = d

nth term = an = - 11

Sum of first n terms = Sn = 66

Let there be n terms in the AP.

Now, Sum of n terms of this arithmetic series is given by:

Sn = [2a + (n - 1)d]

= [a + a + (n - 1)d]

= [a + an]

Therefore sum of n terms of this arithmetic series is given by:

Sn = [22 + (-11)] = 66

11n = 132

n = 12

there are 12 terms in the AP.

Thus nth is the 12th term of the AP.

- 11 = a + (12 - 1)d

- 11 = 22 + 11d

- 11 - 22 = 11d

11d = - 33

d = - 3

Common difference = d = - 3

n = 12, d = - 3

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