Question

If a1=8 and an= 5an-1 + 5 then find the value of a5

Answer 1

a_5 =5780

1) Given the 1st term a_1 =8 and the Recursive formula for this Sequence, let's find the 5th term by plugging and finding each term. Like this:

`\begin{gathered} a_n=5a_(n-1)+5 \\ a_2=5(8)\text{ +5}\Rightarrow a_2=45 \\ a_3=5(45)+5\Rightarrow a_3=230 \\ a_4=5(230)+5\Rightarrow a_4=1155 \\ a_5=5(1155)+5\Rightarrow a_5=5780 \\ (8,\text{ 45, 230, 1155, 5780)} \end{gathered}`

2) Since it is a Recursive Formula we need to recur to the previous term to find the subsequent one. So

`a_5=5780`