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.

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)