How do you determine whether the sequence #10, 8, 6, 4, 2,...# is arithmetic and if it is, what is the common difference?

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Answer 1 · 2017-07-28T08:07:00

common difference is#" "-2#

A sequence is arithmetic if the difference between consecutive terms is constant.

That is you add or subtract the same number to get the next term

In this case we have:

#10,8,6,4,2,...#

the differences between each terms are

#10," "8," "6," "4," "2,...#

#" "darr" "darr" "darr" "darr#

#" "-2,-2,""-2," "-2#

the differences are all the same so it is an Arithmetic sequence

the common difference is #-2#