Find the sum of first 17 terms of an AP whose 4th and 9th terms are - 15 and - 30, respectively.

Let the a be first term and d be common difference of an AP

Given,

4^th term = - 15

a + 3d = - 15 [ using a_n = a + (n - 1)d]

a = - 3d - 15 [ eqn 1]

9^th term = - 30

a + 8d = - 30

- 3d - 15 + 8d = - 30 [ using 1]

5d = - 15

d = - 3

putting this value in eqn 1 we get

a = - 3 (- 3) - 15

= 9 - 15 = - 6

Also we know,

Sum of n terms,

= 17 (- 30)

= - 510