Verified answer

b3-b1=8;

b5-b1=80

b3 = b1*q²

b5 = b1*q⁴

b1*q² - b1 = b1(q² - 1) = 8

b1*q⁴ - b1 = b1(q⁴ - 1) = b1(q² - 1)(q² + 1) = 8(q² + 1) = 80

8(q² + 1) = 80

q² + 1 = 10

q² = 9

q₁₂ = +- 3

b1 = 1

q = 3  q = -3