Question

How do you write the nth term rule for the sequence `4,1,-2,-5,-8,...`?

Answer 1

`n^(th)` term in given sequence is `7-3n`.

Explanation:

This is an arithmetic sequence as the difference `d` between a term and its preceding term is always `-3` as `-3=1-4=-2-1=-5-(-2)=-8-(-5)`.

If first term is `a_1` and common difference in such arithmetic sequence is `d`,

`n^(th)` term is given by `a_1+(n-1)×d`. Hence `n^(th)` term in given series is

`4+(n-1)×(-3)`

= `4-3n+3`

= `7-3n`