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QUESTION

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

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 .

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