Question

Find the 10th term of the geometric sequence.


-0.125, 0.25, -0.5, 1, -2, ...

Answer 1

\(\large\color{black}{ a_n=a_1\times r^{n-1} }\) is the geometirc formula for a(n), so it would be logical to say that:
\(\large\color{black}{ a_{10}=a_1\times r^{10-1} }\)
which gives us: \(\Large\color{red}{ a_{10}=a_1\times r^{9} }\)

Answer 2

you just need to put in the common ratio and the first term into the red equation.

Answer 3

i keep getting the wrong answer :(

Answer 4

i thought the ratio was -.5 because a1/a2?

Answer 5

yes, yes. my bad.

Answer 6

it is just -2.

Answer 7

I was so off. Sorry for confusing you. Saturday must be a very bad day....

Answer 8

\(\large\color{blue}{ a_{10}=a_{1}\times r^9 }\)
\(\large\color{blue}{ a_{10}=a_{1}\times 2^9 }\)

Answer 9

you have the a(1) left.

Answer 10

im confused!

Answer 11

why is it just -2?

Answer 12

well the ratio of a geometric sequence is the number you multiply previous to get the next
in your case the first term is -0.125
to get to 0.25 we multiplied by -2 then again we multiply 0.25 by -2 to get the third term -0.5 and so on

Answer 13

the formula that generate all the terms is given by \(A_n=A_1r^{n-1}\) like @SolomonZelman mentioned above to get the tenth term just evaluate \(A_{10}=-0.125*(-2)^9\)

Answer 14

and its -64

Answer 15

but i am still stuck on the ratio :(

Answer 16

- i don't think so, it shouldn't be negative

Answer 17

why not?

Answer 18

to get the ratio of a geometric sequence all you need is divide the the next term by the previous term 0.25/-0.125 which is -2

Answer 19

but i thought it was a1/a2

Answer 20

it shouldn't be negative since the power is odd \((-2)^9\) this should be negative
and the with -0.125 the negative sign should be gone

Answer 21

hmm no! try -.5 it won't give you 0.25
there is no succession in term

Answer 22

okay thank you

Answer 23

i did get 64 but not negative

Answer 24

welcome^_^
where did you learn that it is a1/a2?

Answer 25

a video in my course :(

Answer 26

hmmm probably doing a different problem but the successive of terms is kept

Answer 27

probably ima look at it again.

Answer 28

but thank you so much for explaining it

Answer 29

welcome!

Answer 30

hmm i think they are doing a1/a2 to find 1/r not r
and then flip 1/r to get the right ratio lol i guess or the problem is set differently
all you need to keep in mind is that the ratio is what need to multiply the previous to get next term

Answer 31

good luck pal:)

Answer 32

okay thank you (: