Question

In an ap the sum of 3rd and 7th term is 6 and the product is 8. Find the sum of first 16 terms.

Answer 1

3rd term + 7th term = 6

a+2d + a+6d = 6

2a + 8d = 6

2(a+4d)=6

a + 4d = 3

a=3-4d

(a+2d)(a+6d)=8

(3-4d+2d)(3-4d+6d)=8

(3-2d)(3+2d)=8

9-4d^2=8

4d^2=1

d^2 = 1/4

d = 1/2

a= 3 - 4d

a = 3 - 4(1/2)

a = 3 - 2

a = 1

sum of 16 terms = 76

$sn \: = \: \frac{16}{2} (2 \times 1 + (16 - 1) \frac{1}{2} ) \\ = 8(2 + \frac{15}{2} ) \\ = 8(2 + 7.5) \\ = 8 \times 9.5 \\ = 76$