Question

PLEASE!!!!! HELP ME!!!!!!

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

Answer 1

`15 = a_1 r^4` (1)

`1 = a_1 r^5` (2)

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

`(r^5)/(r^4)= (1)/(15)`

And then
`r= (1)/(15)`

And then we can find the value
`a_1` and we got from equation (1)

`a_1 = (15)/(r^4) = (15)/(((1)/(15))^4) =759375`

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

`a_n = 759375 ((1)/(15))^n-1 , n=1,2,3,4,...`

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)

Explanation:

the general formula for a geometric sequence is given by:

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

For this case we know that
`a_5 = 15, a_6 = 1`

Then we have the following conditions:

`15 = a_1 r^4` (1)

`1 = a_1 r^5` (2)

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

`(r^5)/(r^4)= (1)/(15)`

And then
`r= (1)/(15)`

And then we can find the value
`a_1` and we got from equation (1)

`a_1 = (15)/(r^4) = (15)/(((1)/(15))^4) =759375`

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

`a_n = 759375 ((1)/(15))^n-1 , n=1,2,3,4,...`

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)