Two terms in a geometric sequence are a5=15 and a6=1.

What is the recursive rule that describes the sequence?

A) a1=50,625; an=an−1⋅15

B) a1=11,390,625; an=an−1⋅15

C) a1=759,375; an=an−1⋅115

D) a1=225; an=an−1⋅5

(1)

(2)

If we divide equations (2) and (1) we got:

And then

And then we can find the value and we got from equation (1)

And then the general term for the sequence would be given by:

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)

Step-by-step explanation:

the general formula for a geometric sequence is given by:

For this case we know that

Then we have the following conditions:

(1)

(2)

If we divide equations (2) and (1) we got:

And then

And then we can find the value and we got from equation (1)

And then the general term for the sequence would be given by:

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)