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Number sequences

# Identify arithmetic and geometric sequences

A sequence is a list of numbers in a certain order. Each number in a sequence is called a term.
• An arithmetic sequence is a sequence of numbers each of which, after the first, is obtained by adding to the preceding number a constant number called the common difference.

Example:
3, 8, 13, 8, 23,... is an arithmetic sequence because each term is obtained by adding 5 to the preceding number.

• A geometric sequence is a sequence of numbers each of which, after the first, is obtained by multiplying the preceding number a constant number called the common rate.

Example:
3, 6, 12, 24, 48,... is a geometric sequence because each term is obtained by multiplying the preceding number by 2.

What kind of sequence is this? 1, 3, 9, 12, 15, ....

In an arithmetic sequence, there is a constant difference between consecutive terms. This means that you can always get from one term to the next by adding or subtracting the same number.

In a geometric sequence, there is a constant multiplier between consecutive terms. This means that you can always get from one term to the next by multiplying or dividing by the same number.

First check if the sequence is arithmetic. There is not a constant difference between consecutive terms. So, the sequence is not arithmetic.

Next check if the sequence is geometric. There is a constant multiplier of 3 between consecutive terms. So the sequence is geometric.

So, the sequence is geometric.