Question

Geometric sequence help? I've tried all answer choices?

Answer 1

please help, what do I do?

Answer 2

To find the 8th term, you multiply the 7th term (a7) by r

a8 = a7*r

a8 = 81*r

how do we find the 9th term?

Answer 3

@jim_thompson5910 multiply the 8th term by r?

Answer 4

correct, so

a9 = a8*r

a9 = 81*r*r ... notice how I replaced 'a8' with 81*r (works because a8 = 81*r)

a9 = 81*r^2

Answer 5

we can keep going as long as we need to

a10 = a9*r

a10 = (81*r^2)*r ... replace a9 with 81*r^2

a10 = 81r^3

Answer 6

we know these two facts

a10 = 3 ... this is given

a10 = 81r^3 ... we just found this

Answer 7

so

81r^3 = 3

r = ??

Answer 8

@jim_thompson5910 .33 or 1/3?

Answer 9

I'd use r = 1/3

Answer 10

\[\Large a_{n} = a*(r)^{n-1}\]
\[\Large a_{n} = a*(1/3)^{n-1}\]
\[\Large a_{7} = a*(1/3)^{7-1}\]
\[\Large a_{7} = a*(1/3)^{6}\]
\[\Large 81 = a*(1/3)^{6}\]
\[\Large 3^4 = a*(1/3)^{6}\]
I'll let you finish. You need to solve for 'a'

Answer 11

I got 59049, I don't know what to do next @jim_thompson5910

Answer 12

oh is my answer a? @jim_thompson5910

Answer 13

before you got 59049, what did you get?

Answer 14

0.00137174211248285322351165980796

Answer 15

idk how you got that

Answer 16

but is A right? @jim_thompson5910

Answer 17

how did you get 0.00137174211248285322351165980796?

Answer 18

.33 repeating to the 6th power, is A right though? @jim_thompson5910

Answer 19

oh i see

Answer 20

I'd do it like this
\[\Large 3^4 = a*(1/3)^{6}\]
\[\Large 3^4*3^6 = a\]
\[\Large 3^{4+6} = a\]
\[\Large 3^{10} = a\]
\[\Large a = 3^{10}\]
so yeah, it's A

Answer 21

thank you

Answer 22

np