IXL - Classify formulas and sequences (Algebra 2 practice)

What kind of sequence is this?

70, 85, 101, 118, ...

arithmetic

geometric

both

neither

ref_doc_title.

Learn with an example

question

What kind of sequence is this?

6, 30, 150, 750, ...

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.

30,

150,

750,

...

+ 24

+ 120

+ 600

Next check if the sequence is geometric. There is a constant multiplier of 5 between consecutive terms. So, the sequence is geometric.

30,

150,

750,

...

× 5

So, the sequence is only geometric.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

MM.1Find terms of an arithmetic sequence

MM.2Find terms of a geometric sequence

MM.4Evaluate recursive formulas for sequences

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