IXL | Identify arithmetic and geometric sequences

A new cookbook is becoming popular. The local bookstore ordered 2 copies in October, 14 copies in November, 98 copies in December, and 686 copies in January. What kind of sequence is this?

arithmetic

geometric

both

neither

ref_doc_title.

Learn with an example

question

What kind of sequence is this?

57, 114, 228, 456, ...

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.

57,

114,

228,

456,

...

+ 57

+ 114

+ 228

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

57,

114,

228,

456,

...

× 2

So, the sequence is only geometric.

$Confetti$

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