Question

Which recursive formula can be used to generate the sequence below,)

Answer 1

Given:

$\begin{gathered} f(1)=6 \\ 6,1,-4,-9,... \end{gathered}$

Required:

We need to find recursive formula

Explanation:

Here we have

$\begin{gathered} f(1)=6 \\ f(2)=1 \\ f(3)=-4 \\ f(4)=-9 \end{gathered}$

Here d is the difference so d must be

$d=f(2)-f(1)=1-6=-5$

now

$\begin{gathered} f(n)=f(1)+(n-1)d \\ f(n)=6-5d+5 \end{gathered}$

now for next term

$\begin{gathered} f(n+1)=f(1)+nd \\ f(n+1)=6-5d \end{gathered}$

compare both equation

Final answer:

$\begin{gathered} f(n)=f(n+1)+5 \\ f(n+1)=f(n)-5 \end{gathered}$

B is the answer