Question

Determine whether each sequence is arithmetic or geometric. Sequence 1: –10, 20, –40, 80, ... Sequence 2: 15, –5, –25, –45, ... Sequence 1 is arithmetic and Sequence 2 is geometric. Both sequences are geometric. Sequence 2 is arithmetic and Sequence 1 is geometric. Both sequences are arithmetic.

Answer 1

The correct answer is c.

Answer 2

1) Is geometric
2) Is arithmetic

How do I know 1 is geometric? If you divide the second number by the one before it and get the same answer when going through the list of numbers it is geometric.. 

For example:

–10, 20, –40, 80

20 / -10 =  -2
-40 / 20 = -2
80 / -40 = -2

They all have -2 when dividing them so it is geometric.


How do I know 2 is arithmetic? If you get the difference of the second number from the number that is before it and it has the same output, it is arithmetic.

For example:

15, –5, –25, –45

(-5) - 15 =  = -20
(-25) - (-5) = -20
(-45) -  (-25) = -20

The arithmetic rule does not work with 1 so 1 is just geometric and the geometric rule does not work with 2 so 2 is just arithmetic. Your answer would be:

Sequence 2 is arithmetic and Sequence 1 is geometric