Question

A recursive rule for an arithmetic sequence is a1=-3;an-1+7

What is the iterative rule for this sequence?

Answer 1

An arithmetic sequence is defined by its first term
`a_1`
its ratio
`r` and the defining formula
`a_n=r* n+a_1`
The first term is given and equal
`a_1=-3`
The ratio is the difference between two consecutive terms, we compute like this:

`a_n=a_(n-1)+7\text{ then } a_n-a_(n-1)=7\\\text{The ratio is the 7}\\\text{The rule is the :}a_n=7n-3`

The correct answer is the second one.