IXL | Identify arithmetic and geometric sequences

On the last day of school, the first student will receive 20 blue pens, the second student will receive 25 blue pens, the third student will receive 30 blue pens, and the fourth student will receive 35 blue pens. What kind of sequence is this?

arithmetic

geometric

both

neither

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Learn with an example

question

Betty is planting flowers in her garden. She plants 6 flowers in the first row, 12 flowers in the second row, 24 flowers in the third row, and 48 flowers in the fourth row. What kind of sequence is this?

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.

12,

24,

48,

...

+ 6

+ 12

+ 24

Next check if the sequence is geometric. There is a constant multiplier of 2 between consecutive terms. So, the sequence is geometric.

12,

24,

48,

...

× 2

So, the sequence is only geometric.

Looking for more? Try these:

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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KK.6Number patterns: mixed review

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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