Question

1) The sum and product of third and seventh terms of an A. P. are 6 and
8 respectively. Find the first term and common difference for the AP.​

Answer 1

Answer:

First term is 5 and common difference is -1/2 ; or first term is 1 and common difference is 1/2.

Step-by-step explanation:

a3 + a7 = 6

a + 2d + a + 6d = 6

2a + 4d = 6

a + 4d = 3              (1)          => a = 3 - 4d.

a3.a7 = 8

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

(3−4d+2d)(3−4d+6d) = 8       [from (1)]

(3−2d)(3+2d)=8

9−4d^2 = 8  

4d^2 = 1

d^2  => 1/4.

d = +/- 1/2.

When d = 1/2

a = 3 - 4d => 3 - 4 (1/2)  =  3 - 2 => 1.

When d = -1/2

a = 3 - 4d => 3 - 4 (-1/2) = 3 + 2 => 5.