Question

How do I write a recursive formula for a sequence ? How can I write a recursive formula for 9, 1, -7, -15

Answer 1

Given:

The sequence is,

$9,1,-7,-15,\ldots\ldots\text{....}$

The common difference is -8.

The recursive formula is expressed as,

$\begin{gathered} a_n=a_{n-1}+d,\text{ for n}\ge2 \\ d=-8 \end{gathered}$

It gives,

$\begin{gathered} a_1=9 \\ a_2=a_1-8=9-8=1 \\ a_3=a_2-8=1-8=-7 \\ a_4=a_4-8=-7-8=-15 \\ \Rightarrow a_n=a_{n-1}-8,\text{ for n}\ge2 \\ a_1=9 \end{gathered}$

Answer:

$\begin{gathered} a_n=a_{n-1}-8,\text{ for n}\ge2 \\ a_1=9 \end{gathered}$