Question

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

Answer 1

ANSWER

The common ratio is 3/2.

EXPLANATION

Given:

$\begin{gathered} \text{ 2nd term of GP: ar = -4} \\ \text{ 5th term of GP: ar}^4\text{ = -}\frac{27}{2} \end{gathered}$

Desired Outcome:

Common ratio

Determine the common ratio

ar = -4

a = -4/r

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

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