Find three consecutive numbers of a geometric sequence where the product of the three numbers is 125 and the sum of the three numbers is 31.?

Just considering the geometric sequence so: 1, 5, 25 the ratio is 5 ... and the sum is 31 and the product is 125 OK!

"three consecutive numbers of a geometric sequence" So they have the form x, rx and r^2x. Each number is r times the previous number. "the product of the three numbers is 125" x * (rx) * (r^2x) = 125 r^3 * x^3 = 125 So r * x = 5. "the sum of the three numbers is 31" x + rx + r^2x = 31 You can use the substitution r = 5/x from rearranging rx = 5. x + (5/x)*x + (25/x^2)*x = 31 x + 5 + (25/x) = 31 x^2 + 5x + 25 = 31. Solve that quadratic for x.