Question

What is the value of the 9th term in the following geometric sequence?3, 12, 48, 192, ...

Answer 1

Given:

The given geometric sequence is 3, 12, 48, 192, ...

Required:

To find the 9th term in the given geometric sequence.

Step-by-step explanation:

The first term is

`a_1=3`

Common ratio is

`\begin{gathered} r=(12)/(3)=4 \\ \\ =(48)/(12)=4 \end{gathered}`

The formula for nth term in geometric sequence is

`a_n=a_1r^(n-1)`

Here

`\begin{gathered} a_9=3(4)^(9-1) \\ \\ =3*4^8 \\ \\ =3*65536 \\ \\ =196608 \end{gathered}`

Final Answer:

The 9th term is 196608.