Question

Find the next term of the geometric sequence 3/2, 3/4, 3/8 , ...

Answer 1

Given:

Geometric sequence:

$\frac{3}{2},\frac{3}{4},\frac{3}{8},.....$

Find-: Next term of the geometric.

Sol:

Common ratio of a geometric sequence.

$r=\frac{a_n}{a_{n-1}}$

A common ratio is:

$\begin{gathered} r=\frac{\frac{3}{4}}{\frac{3}{2}} \\ r=\frac{3}{4}\times\frac{2}{3} \\ r=\frac{1}{2} \end{gathered}$

The next term is:

$a_n=ra_{n-1}$$\begin{gathered} =\frac{1}{2}\times\frac{3}{8} \\ =\frac{3}{16} \end{gathered}$