Question

What is the recursive formula for this geometric sequence?

-3, -21, -147, -1029, ...

Answer 1

`a_(n+1) =7a_(n)`.

If we know the term
`n^(th)` and the common relation, r, of a geometric sequence, you can find the term
`(n+1)^(th)` using the recursive formula
`a_(n+1) =a_(n).r`.

The first term of the geometric sequence is a₁ = -3.

The common relation we have to find the relationship between a term and the term that precedes it.

`r=(-21)/(-3) = 7`

The recursive formula is:

`a_(1) =-3`

`a_(n+1) =7a_(n)`

Answer 2

`a_1=-3\\r=7\\a_n=a_(n-1)\cdot r\\\\ \boxed{a_n=7a_(n-1)}`