IXL | Identify arithmetic and geometric sequences

What kind of sequence is this?

176, 195, 214, 233, ...

arithmetic

geometric

both

neither

ref_doc_title.

Learn with an example

question

What kind of sequence is this?

1, 10, 100, 1,000, ...

arithmetic

geometric

both

neither

key idea

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.

The only way a sequence can be both arithmetic and geometric is if it repeats the same number over and over again.

solution

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

10,

100,

1,000,

...

+ 9

+ 90

+ 900

Next check if the sequence is geometric. There is a constant multiplier of 10 between consecutive terms. So, the sequence is geometric.

10,

100,

1,000,

...

× 10

So, the sequence is only geometric.

Looking for more? Try these:

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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Teacher tools

Work it out

Not feeling ready yet? These can help:

KK.6Number patterns: mixed review

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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