Question

If the sum of first 6 terms is 12 and sum of first 10 terms is 60, then

find the sum of its n terms.

Answer 1

GIVEN

S6 = 12
6/2(A + 6th term) = 12
3(A + A +(n-1)d) = 12
3(2A + (n-1)d) =12

2A+(n-1)d = 4
2A + 5d = 4 ........................(1). ( sum of 6 terms )

S10 = 60
10/2(2A+9d) = 60
2A + 9d = 12 ..................(2)(sum of ten terms)

BY ELIMINATION METHOD,
2A+5d = 4
2A+9d = 12
__________
- 4d = -8

d = 2.................. (3)

SUBSTITUTING EQUATION 3 IN EQ 1

2A +5d = 4
2A + 5(2)=4
2A = 4-10
A = -3

sum of n terms = A + (n-1)d
= -3 + (n-1)(2)
= -3 + 2n -2
= 2n - 5