Question

Find the common ratio and write out the first four terms of the geometric sequence

Answer 1

Given

geometric sequence

$\text{ }\frac{4^{n+1}}{5}$

Find

Common ratio and first four terms of sequence

Explanation

as we have given nth term =

$a_n=\frac{4^{n+1}}{5}$

now put values of n to find the first four terms

$\begin{gathered} a_1=\frac{4^{1+1}}{5}=\frac{16}{5} \\ \\ a_2=\frac{4^{2+1}}{5}=\frac{64}{5} \\ \\ a_3=\frac{4^{3+1}}{5}=\frac{256}{5} \\ \\ a_4=\frac{4^{4+1}}{5}=\frac{1024}{5} \end{gathered}$

common ratio = second term divided by first term

$\begin{gathered} r=\frac{\frac{64}{5}}{\frac{16}{5}} \\ \\ r=4 \end{gathered}$

Final Answer

Common ratio = 4

sequence = 16/5 , 64/5 , 256/5 and 1024/5