Question

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

Answer 1

In the given problem, we have the first and the nth term of an A.P. along with the sum of the n terms of A.P. Here, we need to find the number of terms and the common difference of the A.P.

Here,

The first term of the A.P (a) = 22

The nth term of the A.P (l) = −11

Sum of all the terms

Let the common difference of the A.P. be d.

So, let us first find the number of the terms (n) using the formula,

Further, solving for n

Now, to find the common difference of the A.P. we use the following formula,

We get,

Further, solving for d,

Therefore, the number of terms is and the common difference of the A.P..