Question

Given the sequence of numbers, a4=8, a5=12, a6=16, a7=20, and a8=24.

Which recursive rule can be used to find the nth term of the sequence, an?

a1=4; an=2an−1
a1=4; an=an−1+4
a1=−4; an=an−1+4
a1=−4; an=−2an−1

Answer 1

`a_1=-4, \,a_n=a_(n-1)+4`

Explanation:

Clearly, our common difference is
`d=4`, and we can see that the first term if we work backward from
`a_4` is
`a_1=-4`.

Hence, by using the recursive formula
`a_n=a_(n-1)+d`, we have our final formula as
`a_n=a_(n-1)+4`