The sum of third and seventh terms of an AP is 20 . Find the sum of the first nine

Given:

The sum of third and seventh terms of an AP is 20.

To find:

The sum of the first nine terms.

Solution:

We have, the sum of third and seventh terms of an AP is 20.

       ...(i)

nth term of an AP is

where, a is first term and d is common difference.

      ...(ii)

      ...(iii)

Using (i), (ii) and (iii), we get

        ...(iv)

Now, the sum of first n terms of an AP is

Put n=9 to find the sum of first 9 terms of an AP.

          [Using (iv)]

Therefore, the sum of the first 9 terms is 90.

i would have to say it is c.

step-by-step explanation: