Question

the sum of 3rd and 7th term of an ap is 6 and their product is 8 find the first term and the common difference of the AP

Answer 1

Here ,According to the question

a3+a7=6 1st eq.

and

a3×a7=8 2nd eq.

a3=a+2d

a7=a+6d

putting values of these we get

a+2d+a+6d=6

2a+8d=6

2(a+4d)=2(3)

a+4d=3

a=3-4d 3rd eq.

also we can write 2nd eq. as

(a+2d)×(a+6d)=8

putting value of a from eq.3 we get

(3-4d+2d)×(3-4d+6d)=8

solving it further

(3-2d)(3+2d)=8

3^2-(2d)^2=8

9-4d^2=8

-4d^2=-1

d^2=1/4

d=+1/2 and -1/2

that's your answer

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