Question

The AP in which 4th term is -15 and 9th term is -30. Find the sum of the first 10 numbers.
The answer is -195.
Please solve this with proper steps.

Answer 1

Here is your solution

Given :-

The AP in which 4th term is -15
I. e
a4= (a+3d)= -15 ..................... (1)

9th term is -30
I.e
a9= (a+8d)= -30..................... (2)

on subtracting equation (1) from (2)

(a+3d) - (a +8d) = -15 + 30
-5d= 15
d=-15/5
d= -3

put in value of d in equation (1)

a+3d = -15
a-9= -15
a= -6

S10=?

Sn=n/2(2a+(n-1)d)
S10=10/2(2(-6)+(10-1)-3)
S10=5(-12-27)
S10=5(-39)
S10= -195

So, the sum of first 10 terms of this A.P. is -195,

Hope it helps