Question

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

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

Answer 1

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-(-15) = 29`

`T_3-T_2 =-15-(-44) = 29`

`T_2-T_1 = -44 -(-73) = 29`

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

This is therefore an arithmetic sequence.