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

1 Answer
Dec 14, 2015

Answer:

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#.