Question

Determine if the following sequences are arithmetic, geometric or neither. if the sequence is arithmetic, find the common difference. if the sequence is geometric, find the common ratio. a. 1, 3, 6, 10, 15, ... b. 40, 43, 46, 49, 52, ...

Answer 1

To find if it's arithmetic, subtract a number from the next number.
If you do it a few times and all differences are equal, it is arithmetic.

Answer 2

Start with part a.
What is 3 - 1 = ?
What is 6 - 3 = ?

Answer 3

3-1=2
6-3=3

Answer 4

b is arithmetic but a is not. i think a is geometric

Answer 5

Correct for b.
Since all the differences are equal in part b., it is arithmetic.
52 - 49 = 3
49 - 46 = 3
46 - 43 = 3
etc.

Answer 6

You are also correct that part a,. is not arithmetic.
Now we need to see if part a is geometric.

Answer 7

To test for a geometric sequence, you divide each number by the previous number.
If all results are equal, it is geometric. As soon as you find two results not equal you can stop, and it is not geometric.

Answer 8

What is 15/10 = ?
What is 6/2 = ?

Answer 9

15/10=1
6/2=3

Answer 10

Sorry. I made a mistake, but you made one too.
We need:
15/10 = 1.5
6/3 = 2

Answer 11

As you can see, when we divided two sets of consecutive numbers in the sequence, we got different quotients, 1.5 and 2.
That means it is not a geometric sequence.

Answer 12

The answer is:
a. neither
b. arithmetic; common difference = 3

Answer 13

correct mathstudent. a is neither.

Answer 14

Ok thank you mathstudent55 :)

Answer 15

You're welcome.