Question

Determine the common ratio of a geometric sequence if the second term is -4 and the fifth term is -27/2.A- -3/2B- 3/2C- -27/16D- 27/16

Answer 1

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is

`a_n=a_1r^(n-1)`

The value r is called the common ratio.

On the sequence of our problem, we know the second and fifth term. If we substitute those values on the general term presented, we have

`\begin{gathered} a_2=a_1r^(2-1)=a_1r=-4 \\ a_5=a_1r^(5-1)=a_1r^4=-(27)/(2) \end{gathered}`

If we divide the fifth term by the second term, we're going to have

Solving for r, we have

`\begin{gathered} r^3=((-27\/2))/((-4)) \\ r^3=(27)/(8) \\ r=\sqrt[3]{(27)/(8)} \\ r=(3)/(2) \end{gathered}`

The common ratio is 3/2.