Question

The sum of third and seventh term of an A. P. is 6 and their product is

8. Find the first term and the common difference of the A. P.

Answer 1

Answer:

The 3rd term of an AP is a+2d and the 7th term is a+6d. So we have

the sum of 3rd term and 7th term = a+2d+a+6d = 6, or

2a+8d = 6, or

a + 4d = 3 …(1)

Their product is (a+2d)*(a+6d) = 8 …(2)

From (1), a = 3–4d. Put that in (2) to get

(a+2d)*(a+6d) = 8, or

(3–4d+2d)*(3–4d+6d) = 8, or

(3–2d)*(3+2d) = 8, or

9–4d^2 = 8, or

4d^2 = 1, or

d^2 = 1/4, or

d = 1/2.

From (1), a = 3–4d = 3–2 = 1.

The sum of the first 16 terms

S16 = (n/2)[2a+(n-1)d]

= (16/2)[2*1 + (16–1)*1/2]

= 8[2+15/2]

= 8 *19/2

= 76. Answer.