Question

The sum of the third and seventh terms of an AP is 6, and their product is 8. What is the sum of the first 20th terms of the AP?

Answer 1

a+2d +a+6d = 6
2a+8d=6
a+4d = 3
a=3-4d-(1)
(a+2d)(a+6d)=8
put value of a from (1)
(3-2d)(3+2d)=8
9-4d^2 = 8
4d^2 =1
d^2 =1/4
d=1/2
a = 3 -4×1/2
a=1
S20 = 10 (2+19×1/2)
=> 115