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

1 Answer
May 10, 2016

Answer:

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#

#color(white)()#
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.