Question

Determine the common ratio of a geometric sequence if the second term is -4 and fifth term is -27/2

Answer 1

The common ratio is 3/2.

Step-by-step explanation

Given:

`\begin{gathered} \text{ 2nd term of GP: ar = -4} \\ \text{ 5th term of GP: ar}^4\text{ = -}(27)/(2) \end{gathered}`

Desired Outcome:

Common ratio

Determine the common ratio

ar = -4

a = -4/r

`\begin{gathered} substitute\text{ a} \\ ar^4\text{ = -}(27)/(2) \\ (-(4)/(r))r^4\text{ = -}(27)/(2) \\ -4r^3\text{ = -}(27)/(2) \\ divide\text{ bothe sides by -4} \\ r^3\text{ = }(27)/(8) \\ take\text{ cube root of both sides} \\ r^3\text{ = }(3^3)/(2^3) \\ r\text{ = }(3)/(2) \end{gathered}`

Hence, the common ratio of the geometric sequence is 3/2.