Question

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

Answer 1

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`.