Question

The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.

Answer 1

We know that,

a_n = a + (n − 1) d

a₃ = a + (3 − 1) d

a₃ = a + 2d

Similarly, a₇ = a + 6d

Given that, a₃ + a₇ = 6

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

2a + 8d = 6

a + 4d = 3

a = 3 − 4d (i)

Also, it is given that (a₃) × (a₇) = 8

(a + 2d) × (a + 6d) = 8

From equation (i),

From equation (i),