Question

What is the recursive formula when given the explicit formula for the following geometric sequence?

a^n = 12(33)^n-1

Answer 1

`\left \{ {{a_1=12} \atop{a_n=a_(n-1)*(33)}} \right.`

Explanation:

For a geometric sequence the explicit formula has the following formula:

`a_n=a_1(r)^(n-1)`

Where
`a_1` is the first term in the sequence, and r is the common ratio and
`a_n` is the nth term of the sequence:

In this case we have the following sequence

`a_n = 12(33)^(n-1)`

Then:

`a_1=12\\r=33`

The recursive formula for the geometric sequence has the following formula

`\left \{ {{a_1} \atop {a_n=a_1*r}} \right.`

Where
`a_1` is the first term in the sequence, and r is the common ratio and
`a_n` is the nth term of the sequence:

In this case the recursive formula is:

`\left \{ {{a_1=12} \atop{a_n=a_(n-1)*(33)}} \right.`