assuming an AP whose first term is a and the common difference is d

To find: the sum of first 10 terms

Given 12^th term is - 13

So, a + 11d = - 13...(i)

Given the sum of first four terms is 24

So 4a + 6d = 24…(ii)

Solving (i) and (ii) we get

a = 9 and d = - 2

we know that the sum of AP is given by the formula:

substituting the values in the above equation

s = 0