Question

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

Answer 1

Given

geometric sequence

`\text{ }(4^(n+1))/(5)`

Find

Common ratio and first four terms of sequence

Step-by-step explanation

as we have given nth term =

`a_n=(4^(n+1))/(5)`

now put values of n to find the first four terms

`\begin{gathered} a_1=(4^(1+1))/(5)=(16)/(5) \\ \\ a_2=(4^(2+1))/(5)=(64)/(5) \\ \\ a_3=(4^(3+1))/(5)=(256)/(5) \\ \\ a_4=(4^(4+1))/(5)=(1024)/(5) \end{gathered}`

common ratio = second term divided by first term

`\begin{gathered} r=((64)/(5))/((16)/(5)) \\ \\ r=4 \end{gathered}`

Final Answer

Common ratio = 4

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