The sum of a threee consecutive term of an AP is 6 and the product is -90.find the terms

Question

Arithmetic progression

Answer 1

The three terms can be represented by a, a+d, a+2d, so 3a+3d=6 and a+d=2.

The product is a(a+d)(a+2d)=-90. But a+d=2 so a(a+2d)=-45. Also d=2-a so we can substitute for d:

a(a+4-2a)=-45; a(4-a)=-45; 4a-a^2=-45; a^2-4a-45=0=(a-9)(a+5), so a=9 or -5 and d=2-a=-7 or 7.

The series is ..., 9, 2, -5, ... or ..., -5, 2, 9, ...