Question

What is the next number in this geometric sequence?

-3.42, 10.26, -30.78, 92.34, , ...

A. 277.02
B. 184.68
C. -277.02
D. -184.68

Answer 1

compare the terms and find the common ratio...

\[\frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} = ...\]

Answer 2

when you find the common ratio, multiply it by the last term

Answer 3

ok i don't get the a2/a1 = a3/a2 do i put the sequences in there? -3.42/10.26=-30.78/92.34?

Answer 4

so what value you you get with each fraction...

is 10.26/3.42 = the same as -30.78/10.26 = ...?

it you say yes, you have the common ratio

Answer 5

wouldn't it be -3.42?

Answer 6

the 2nd term in a geometric sequence is the 1st term times the common ratio.

if you know the 1st and 2nd terms... as in this question.

divide the 2nd term by the 1st term to find the common ratio.

then the 3rd term is the 2nd term times the common ratio...

so again find the common ratio to check.

Answer 7

this is what it looks like

-3.42 x r = 10.26 find r

to check use the 2nd and 3rd terms

10.26 x r = -30.78

Answer 8

r = -3 @campbell_st

Answer 9

that's correct... that is the common ratio... and every term in a geometric series is mutiplied by that value.

so take the last term, 92.34 and multiply it by -3 for you answer

Answer 10

Thanks for your help!!