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

Question

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

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Answer 1 · 2017-04-03T21:39:16

This is an arithmetic sequence with $d = 29$ $d= 29$

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

We ask: Is $T_{4} - T_{3} = T_{3} - T_{2} = T_{2} - T_{1} ?$ $" "T_4-T_3 " = "T_3-T_2" = "T_2-T_1?$

$T_{4} - T_{3} = 14 - (- 15) = 29$ $T_4-T_3 = 14-(-15) = 29$

$T_{3} - T_{2} = - 15 - (- 44) = 29$ $T_3-T_2 =-15-(-44) = 29$

$T_{2} - T_{1} = - 44 - (- 73) = 29$ $T_2-T_1 = -44 -(-73) = 29$

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

This is therefore an arithmetic sequence.