Question

The explicit rule for a sequence is given.

an=3(16)n−1



Enter the recursive rule for the geometric sequence.

a^1=

a^n=

Answer 1

`a_(1)=3`

`a_(n)=16a_(n-1)`

just use the standart recursive for geometric sequence

Answer 2

`a_1=3`

`a_n = 16 \cdot a_(n-1)`

Explanation:

The explicit formula for the geometric sequence is given by:

`a_n =a_1 \cdot r^(n-1)` ....[1]

where

`a_1` is the first term

r is the common ratio of the consecutive terms

n is the number of terms

Given that:

The explicit rule for a sequence is given. by:

`a_n =3 \cdot (16)^(n-1)`

On comparing with equation [1] we have;

`a_1=3` and r = 16

Use the recursive formula for the geometric sequence is:

`a_n = r \cdot a_(n-1)`

Substitute the given values we have;

`a_n = 16 \cdot a_(n-1)`

therefore, the recursive rule for the geometric sequence is,
`a_n = 16 \cdot a_(n-1)`