Question

What is the nth term of the geometric sequence that has a common ratio of 6 and 24 as its third term? A. ` ` ` ` `a_(n)=24(6)^(n-1)` B. `a_n=2/3(6)^(n-1)` C. `a_(n)=24(6)^n` D. `a_(n)=3/2(6)^(n-1)`

Answer 1

B. `a_n=2/3(6)^(n-1)`

Answer 2

Option B. is the answer.

Explanation:

Explicit formula of a geometric sequence is
`a_(n)=a(r)^(n-1)`.

As given in the question

common ratio r = 6

and
`a_(3)=6`

`a_(3)=a(6)^(3-1)`

`24=a(6)^(2)`

`a=(24)/(36)`

`a=(2)/(3)`

Now we put this values in the explicit formula to get the nth term of the sequence.

`a_(n)=(2)/(3)(6)^(n-1)`

Option B is the answer.