Question

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle term is 7 : 15 find the Number ?​

Answer 1

let the four terms

be

a-3d , a-d , a+d ,a+3d

sum = 32

a-3d +a-d +a+d +a+3d=32

4a=32

a=8

also

(a-3d)(a+3d)/(a-d)(a+d)=7/15

(a²-9d²)15=(a²-d²)7

15a²-135d²=7a²-7d²

but a= 8

15×64-7×64=128d²

d²=64×8/128

d²=4

so d=+4 or d=-4

so no. are

a-3d=8-12or8+12=-4or20

a-d=8-4or8+4=4or12

a+d=8+4or8-4=12or4

a+3d=8+12or8-12=20or-4

Answer 2

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