about Arithmetic progression

Question

the sum of first 4 terms of an AP is 32. the ratio of products of the first and last term to the 2 middle terms is 7:15. What is the AP?

Answer 1

a₁+a₂+a₃+a₄=32

a₁a₄/a₂a₃=7/15

 

a₁+(a₁+d)+(a₁+2d)+(a₁+3d)=32

15a₁(a₁+3d)=7(a₁+d)(a₁+2d)

 

4a₁+6d=32

8a₁²+45a₁d-21a₁d-14d²=0

(Solve it fo a1 and d)

a₁=2, d=4 or a₁=14, d=-4

 

d=4;  2, 6, 10, 14.

d=-4; 14, 10, 6, 2.