Question

in an AP the sum of 3rd and 7th term is 6 and their product is 8 find the first term and common differences of the A. P

Answer 1

Let a be first term and d be the common difference
3rd term + 7th term = 6
a +2d + a + 6d = 6
ie a + 4d = 3
ie a = 3-4d.....(1)
Also
(a+2d)(a+6d)=8
(3-4d+2d)(3-4d+6d)=8
(3-2d)(3+2d)=8
9-4d^2= 8
d^2=1/4
d=1/2
And a=3-4*(1/2)=1

Answer 2

Here is your solution

Given:-

The sum of 3rd term and 7th term
=>a+2d+a+6d = 6
=>2a+8d = 6
After common taking
a + 4d = 3
a=3-4d ..................….......(1)

Their product is

(a+2d)×(a+6d) = 8 .........…(2)

Putting value of a = 3–4d in equation (2) to get

=>(a+2d)×(a+6d) = 8

=>(3–4d+2d)×(3–4d+6d) =8

=>(3–2d)×(3+2d) = 8

=>9–4d^2 = 8

=>4d^2 = 9-8

=>4d^2 = 1

=>d^2 = 1/4

=>d = 1/2.✔

From (1) a = 3–4d
a=> 3–4×1/2
a=>3-2
a=> 1✔



Hope it helps you