Question

(2) 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

let the first term of the AP be a
and common difference of the AP be d

since it is given that the sum of the 3rd term and 7th term of the AP is 6

so the system of equation can be written as

a+ 2d+ a+ 6d=6
2a + 8d = 6
(dividing whole equation by 2)
a+4d=3 --------(1)

secondly there is a given that product of third term and seventh term is 8

so system of equation can be written as
(a+2d)(a+6d)=8
a^2+6ad+2ad+12d^2=8
a^2+8ad+12d^2=8---------(2)

from first and second equation
we can find the value of a and d

Answer 2

a+2d + a + 6d = 6

2 a + 8d = 6

a + 4d = 3 -----1

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

u can solve now ..