Question

One term of a geometric sequence is a4=135. The common ratio is r=3. Write an explicit rule for the nth term.

Answer 1

`a_(n) = 5 * 3^(n-1)`

Explanation:

To find the nth term of a geometric sequence, you have the general formula:

`a_(1) *r^(n-1)`

where a1 is the first term and r is the common ratio. In order to find the 4th term, we can substitute what we have(n is 4 because we are looking for the fourth term):

135 =
`a_(1) * 3^(4 - 1)`

135 =
`a_(1) * 3^3`

135 =
`27a_(1)`

`a_(1) = 5`

Now, we can substitute the first term back in:

`a_(n) = 5 * 3^(n-1)`