IXL | Identify arithmetic and geometric sequences

What kind of sequence is this?

47, 62, 77, 92, ...

arithmetic

geometric

both

neither

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Learn with an example

question

What kind of sequence is this?

98, 113, 128, 143, ...

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 a constant difference of 15 between consecutive terms. So, the sequence is arithmetic.

98,

113,

128,

143,

...

+ 15

Next check if the sequence is geometric. There is not a constant multiplier between consecutive terms. So, the sequence is not geometric.

98,

113,

128,

143,

...

×
113
98

×
128
113

×
143
128

These multipliers are not all the same:

113

≈

1.153

128

113

≈

1.133

143

128

≈

1.117

So, the sequence is only arithmetic.

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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