Respuesta :
State the given in the question
[tex]\begin{gathered} a_1=9 \\ a_n=4a_{n-1} \end{gathered}[/tex]State what is to be found: We are to find the fifth term
[tex]\begin{gathered} \text{value of:} \\ a_5 \end{gathered}[/tex]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:
[tex]\begin{gathered} a_n=4a_{n-1} \\ a_2=4a_{2-1} \\ a_2=4a_1 \\ a_1=9 \\ a_2=4\times9 \\ a_2=36 \end{gathered}[/tex]The third term is as calculated below:
[tex]\begin{gathered} a_n=4a_{n-1} \\ a_3=4a_{3-1} \\ a_3=4a_2 \\ a_2=36 \\ a_3=4\times36 \\ a_3=144 \end{gathered}[/tex]The fourth term is as calculated below:
[tex]\begin{gathered} a_4=4a_{4-1}=4a_3 \\ a_3=144 \\ a_4=4\times144 \\ a_4=576 \end{gathered}[/tex]The fifth term is as calculated below:
[tex]\begin{gathered} a_5=4a_{5-1}=4a_4 \\ a_4=576 \\ a_5=4\times576 \\ a_5=2304 \end{gathered}[/tex]Hence, the fifth term a₅= 2304
