Question

Which of the following sequences is an arithmetic sequence?

A. {-10,5,-2.5,1.25,...}
B. {100,20,4,0.8,...}
C. {1,4,16,48,...}
D. {-10,-3.5,3,9.5,...}

Answer 1

D

Explanation:

For a sequence to be an arithmetic sequence, it must have a common difference. In other words, it must either go down by the same number or up by the same number.

Let's look at the choices:

A. {-10,5,-2.5,1.25,...}

-10 to 5, that went up by 15. It has to keep going up by 15 to be arithmetic. However 5+15 is not -2.5 so it isn't arithmetic.

B. {100,20,4,0.8,...}

100 to 20, that went down by 80. Since 20-80 is not 4, then this sequence is not arithmetic.

C. {1,4,16,48,...}

1 to 4, that went up by 3. 4+3 is not 16 so this is not arithmetic.

D. {-10,-3.5,3,9.5,...}

-10 to -3.5, that went up 6.5.

-3.5+6.5=3

3+6.5=9.5

This is arithmetic. It keeps going up by 6.5.