Question

What is the 7th term of the geometric sequence 3, 9, 27,...?

Answer 1

A geometric sequence has a constant ratio (common ratio) between consecutive terms.

For 3, 9, 27, ... the common ratio is 3 because:
3 X 3 = 9
9 X 3 = 27

So to find the 7th term you can do it two ways:

One way:
3 is the 1st term, 9 is the 2nd term, 27 is the 3rd term so then
4th term: 27 X 3 = 81
5th term: 81 X 3 = 243
6th term: 243 X 3 = 729
7th term: 729 X 3 = 2,187

Another way:
You can use the explicit formula `a_n = a_1 *r^(n-1)`, where `a_n` is the nth term, `a_1` is the first term, n is the number of the term, and r is the common ratio

so `a_7 = 3 * 3^ (7-1)`
`a_7 = 3 * 3^ (6)`
`a_7 = 3 * 729`
`a_7 = 2,187`

Both ways get you to the same answer that the 7th term in that geometric sequence is 2, 187 .