# Geometric sequences

A geometric sequence is a number sequence in which the ratio between two consecutive terms is constant. Each term is found by multiplying previous term with a number called the common ratio.

# 2,4,8,16,32,...

Above is a geometric sequence, and the common ratio of two consecutive terms is 2. This number is marked by q. The sequence would continue 64,128,256,512, ...

Example 1

The first term of a geometric sequence is 2 and the second term is 6. Find the next two terms of the sequence. ### General term In a geometric sequence, we have a common ratio q that multiplies the term of the sequence to get the next term. To get the second term we multiply the first term by q. To get the third term we multiply the first term twice by q. The fourth term is obtained by multiplying the first term three times by q . And so on.

We can get any term when we multiply the first term by q to the power less than one of the order number of that term. Example 2

The first term of a geometric sequence is 2 and the second term is 6. Find the tenth term of the sequence. Turn on the subtitles if needed