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

Jun 5, 2017

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

#### Explanation:

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 ${T}_{6} - {T}_{4} = {T}_{4} - {T}_{2}$???

$26 - 16 = 10 \text{ and } 16 - 8 = 8$

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

We could also solve for $d$:

For ${T}_{6} \mathmr{and} {T}_{4} : \text{ "2d = 26-16 = 10" } \rightarrow d = 5$

For ${T}_{4} \mathmr{and} {T}_{2} : \text{ "2d = 16-8 = 8" } \rightarrow d = 4$