Is the following a geometric sequence 3, 9, 27, 81,…?

1 Answer
sente
Dec 14, 2015

Yes. It is a geometric sequence with initial term a_0 = 3 and common ratio r = 3.

Explanation:

A geometric sequence is a sequence of the form

a_0, a_0r, a_0r^2, a_0r^3, ..., a_0r^n, ...

where a_0 is the first term in the sequence and r is the common ratio between terms.

Looking at the given sequence, we can write it as

3, 3*3^1, 3*3^2, 3*3^3, ...

which matches the pattern for the first term a_0 = 3 and common ratio r = 3.

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