Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.

Answer 1

an=9(4^n-1)

Explanation:

Answer 2

`a_n=9(4^(n-1))`

Explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant, called the common ratio (r)

In this problem we have

`a_2=36\\ a_5=2,304`

Remember that

`a_2=a_1(r)` ----->
`36=a_1(r)` -----> equation A

`a_5=a_4(r)`

`a_5=a_3(r^(2))`

`a_5=a_2(r^(3))`

Substitute the values of a_5 and a_2 and solve for r

`2,304=36(r^(3))`

`r^(3)=2,304/36`

`r^(3)=64`

`r=4`

Find the value of a_1 in equation A

`36=a_1(4)`

`a_1=9`

therefore

The explicit rule for the nth term is

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

substitute

`a_n=9(4^(n-1))`