Question

What is the common difference of 1, 2, 4, 8, 16,...?

Answer 1

This sequence has a common ratio (`2`), rather than a common difference. It is a geometric sequence, not an arithmetic one.

Explanation:

Arithmetic sequences have a common difference. That is, the difference between any two consecutive terms is constant.

For example:

`5, 8, 11, 14, 17`

is an arithmetic sequence with common difference `3`.

We note that:

`8-5 = 11-8 = 14-11=17-14 = 3`

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Geometric sequences have a common ratio. That is, the ratio between any two consecutive terms is constant.

For example:

`1, 2, 4, 8, 16`

is a geometric sequence with common ratio `2`.

We note that:

`2/1 = 4/2 = 8/4 = 16/8 = 2`

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The infinite sequence `1, 2, 4, 8, 16,...` is a geometric sequence if it continues in similar fashion in the "...", doubling every step.