# Is the following sequence arithmetic? If so, identify the common difference. –73, –44, –15, 14, . . .

## yes, -31 yes, -29 no yes, 29

Apr 3, 2017

This is an arithmetic sequence with $d = 29$

#### Explanation:

If a sequence (or progression) is arithmetic, then the difference between any two terms is the same.

We ask: Is " "T_4-T_3 " = "T_3-T_2" = "T_2-T_1?

${T}_{4} - {T}_{3} = 14 - \left(- 15\right) = 29$

${T}_{3} - {T}_{2} = - 15 - \left(- 44\right) = 29$

${T}_{2} - {T}_{1} = - 44 - \left(- 73\right) = 29$

In each case the difference is the same. This value is called the common difference: $d = 29$

This is therefore an arithmetic sequence.