Question

Find R:

Answer 1

\[\sum_{k=1}^{\infty} 3r ^{k-1} =5\]

Answer 2

@hartnn Could u possibly help with this?

Answer 3

yes

Answer 4

Ok great. How should I approach the problem?

Answer 5

do you know the formula ? .....
wait , what is the topic ? is this related to geometric sequences ?

Answer 6

Yes it is

Answer 7

cool,
so can you find the terms ? 1st term, 2nd terms, .... ?

Answer 8

Yes, the 1st term is 1, the 2nd term is 3, the 3rd term is 9

Answer 9

where did the 'r' go ? :O

Answer 10

See I dont think i'm doing it correctly :O

Answer 11

3r^0, 3r^1, 3r^2, 3r^3

Answer 12

I dont understand what to do with the r variable.

Answer 13

ok, so find the common ratio now, know what that is ?

Answer 14

would it be 3?

Answer 15

no,
see common ratio = 2nd term/1st term = 3rd term/2nd term =.... so on

so, whats
3r/3 = ... ?
3r^2/3r = ... ?

Answer 16

So just r?

Answer 17

yes! thats your common ratio,
now you are almost done,

3,3r,3r^2 .... is an infinite geometric series.
and the sum is given by
\(\Huge S_\infty=\dfrac{a}{1-r} \)


where a is 1st term and r is common ratio

so your sum will be ?

Answer 18

Ok, im familiar with the sum formula. It would be.. no such value?

Answer 19

1/1-1 = 1/0

Answer 20

ohhhhh wait.

Answer 21

what is 'no such value?'

see, a = 3 right ? , r= r
so,
3/(1-r) = 5

find r from here

Answer 22

yeah. i was thinking r = 1. lol

Answer 23

r = 2/5

Answer 24

correct! :)

Answer 25

Ok I see what you did there. Thanks so much. I now understand it.

I was making it more complicated than what it actually was.

Answer 26

ok, you're welcome ^_^