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

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

1 Answer
Apr 3, 2017

This is an arithmetic sequence with d= 29d=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? T4T3 = T3T2 = T2T1?

T_4-T_3 = 14-(-15) = 29T4T3=14(15)=29

T_3-T_2 =-15-(-44) = 29T3T2=15(44)=29

T_2-T_1 = -44 -(-73) = 29T2T1=44(73)=29

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

This is therefore an arithmetic sequence.