# 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.

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