Question

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

Answer 1

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. 

Answer 2

Answer:

The answer would actually be: $2(\frac{1}{3})^{n-1}$

Step-by-step explanation:

I just took the test.