Question

The recursive rule for a geometric sequence is given. a1=2;an=13an−1

Answer 1

The answer would actually be:
`2((1)/(3))^(n-1)`

Explanation:

I just took the test.

Answer 2

The complete question is:
The recursive rule for a geometric sequence is given.
`a_(1)=2`;
`a_(n)= 13*a_(n-1)`. Enter the explicit rule for the sequence.

Solution:
We are given

`a_(1)=2 \\ \\ a_(n) = a_(n-1)`

Explicit rule of geometric sequence is of the form:


`a_(n) = a_(1) (r)^(n-1)`

Using the given recursive sequence, we can find r.


`a_(1)=2`

`a_(2)=13* a_(1)=13*2=26`

r = Ratio of consecutive two terms of Geometric series.
So,
r = 26/2 = 13

Therefore,


`a_(n)=2(13)^(n-1)` is the explicit rule for the given geometric sequence.