Question

in an ap the first term is 22 nth term is -11and the sum of first n terms is 66 find n and d , the common difference

Answer 1

Given first term = a = 22
n th term = -11

We know that nth term = a + (n-1)d

Now , 22+(n-1)d = -11

=>( n-1)d = -11-22

=> (n-1)d = -33

Given Sum of first n terms = 66 .

Sum of n terms = n/2 ( 2a + (n-1)d )

=> n/2 (2*22-33)

=> n/2(11)

=> 11n/2

According to the question , 11n/2 =66

11n = 66 * 2

n = 132/11=12

n = 12 .

Now substituting , ( n - 1)d = -33

=> (12-1)d = -33

=> 11d = -33

=> d = -3 .

Therefore , n = 12 , d = -3

Hope helped !^^