How do you tell whether the sequence with the terms #a_2=8, a_4=16, a_6=26# is arithmetic?

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Answer 1 · 2017-06-05T09:08:12

There is NOT a constant difference, therefore the sequence is NOT arithmetic.

If a sequence is arithmetic, then the difference between consecutive terms is the same.

In this case, every second term is given, so the difference will be twice the common difference.

Is # T_6 -T_4 = T_4 - T_2#???

#26-16 = 10" and " 16-8 =8#

There is NOT a constant difference, therefore the sequence is NOT arithmetic.

We could also solve for #d#:

For #T_6 and T_4:" "2d = 26-16 = 10" "rarr d = 5#

For #T_4 and T_2:" "2d = 16-8 = 8" "rarr d =4#