Question

Tell whether the sequence
1/3, 0, 1, -2… is arithmetic, geometric, or neither.

Find the next three terms of the sequence.

A. neither; 7, -20, 61
B. geometric;7, -20, 61
C. arithmetic; -13, 113, 3
D. geometric;-313, -559, -9727

Answer 1

arithmetic sequences are sequences in which you add a positive or negative number to get from one number to the next

geometric is where you multiply by a common number known as the ratio to get from one number to the next

Answer 2

I know, but I'm not sure how they started with a positive fraction for this one, and ended with a negative whole number

Answer 3

\[(-10+9 n-2 n^2)/(-13+4 n)\]

Answer 4

@optiquest I'm not sure what that equation has to do with this?

Answer 5

what equation are you using to find each term

Answer 6

geometric series where a is the first number in sequence, r is the ratio

a, ar, ar^2

to get the ratio you do the current term divided by the term before it

ar/a = r
ar^2/ar=r

this tells you the common ratio, if it is the same throughout, then it is geometric

arithmetic where a is the first number, d is the number you add on

a, a+d, a+d+d,
so we have
a, a+d, a+2d

to find out d we do the current term subtract the term before it

a+d - a=d
a+2d - (a+d)=d

Answer 7

if you cant find a common difference, or common ratio, then it is neither

Answer 8

Well. it can't be geometric because if it was, anything after 0 would still be 0..

Answer 9

And for being arithmetic, I don't think it could be that, because its not a consistent change..

Answer 10

then you got your answer

Answer 11

Thank you!

Answer 12

This is for a different question, but if you're multiplying to get to the next term, that's geometric? @amorfide

Answer 13

aslong as it is multiplying by the same number, to get from one number to the next yes

Answer 14

a, ar, ar*r, ar*r*r

Answer 15

Okay, thank you!

Answer 16

you can't have
a. ar. arb, arbc
where r, b and c are different multipliers

Answer 17

So if it's 3, 12, 36.. That would be geometric, or no..?

Answer 18

no

Answer 19

21/3=4
36/12=3

Answer 20

Oh.. but it's being multiplied by 4 each time..

Answer 21

no it is not

Answer 22

3r=12
r=4

12r=36
r=3

Answer 23

I thought you were supposed to start from the beginning to find a pattern? That's what I've always been taught..

Answer 24

yes we did start from the beginning

Answer 25

your sequence is 3,12,36

Answer 26

geometric series is
a, ar, ar^2

Answer 27

a=3

Answer 28

I see what I did wrong now.. But either way this sequence isn't going to be geometric right?

Answer 29

3r=12

12r=36

you get different value for r

Answer 30

it is only geometric if you get the same r value

Answer 31

Okay, thank you