Question

If a1= 9 and An= 4An-1 then find the value of a5

Answer 1

State the given in the question

`\begin{gathered} a_1=9 \\ a_n=4a_(n-1) \end{gathered}`

State what is to be found: We are to find the fifth term

`\begin{gathered} \text{value of:} \\ a_5 \end{gathered}`

In other to get the fifth term, we will first find the second, the third, and the fourth term

Find the second term as shown below:

`\begin{gathered} a_n=4a_(n-1) \\ a_2=4a_(2-1) \\ a_2=4a_1 \\ a_1=9 \\ a_2=4*9 \\ a_2=36 \end{gathered}`

The third term is as calculated below:

`\begin{gathered} a_n=4a_(n-1) \\ a_3=4a_(3-1) \\ a_3=4a_2 \\ a_2=36 \\ a_3=4*36 \\ a_3=144 \end{gathered}`

The fourth term is as calculated below:

`\begin{gathered} a_4=4a_(4-1)=4a_3 \\ a_3=144 \\ a_4=4*144 \\ a_4=576 \end{gathered}`

The fifth term is as calculated below:

`\begin{gathered} a_5=4a_(5-1)=4a_4 \\ a_4=576 \\ a_5=4*576 \\ a_5=2304 \end{gathered}`

Hence, the fifth term a₅= 2304