Question

Find the sum:

5-(5/3)+(5/9)-(5/27)+(5/81)-......

Answer 1

so I know the formula to find the ratio is Sn+1/Sn and i thought i found the ratio and i got -1/3 which is probably wrong :(

Answer 2

To find out if a sequence is arithmetic when given 4 terms:

1. Subtract 2nd term minus 1st term.
2. Subtract 3rd term minus 2nd term.
3. Subtract 4th term minus 3rd term.

If all three are the same then the sequence is arithmetic,
with d = common difference = this value.

To find out if a sequence is geometric when given 4 terms:
1. Divide 2nd term by 1st term.
2. Divide 3rd term by 2nd term.
3. Divide 4th term by 3rd term.

If all three are the same then the sequence is geometric,
with r = common ratio = this value.

-----------------------

First we test to see if it's an arithmetic sequence:

1. Subtract 2nd term minus 1st term. (5/9) - (-5/3) = 20/9
2. Subtract 3rd term minus 2nd term. (-5/27) - (5/9) = -20/27
3. No need to subtract 4th term minus 3rd term since those aren't the
same. We know it is not an arithmetic sequence.

So that rules out choices 2 and 4. So it's between 1 and 3.

Next we test to see if it's a geometric sequence:

1. Divide 2nd term by 1st term. (5/9)÷(-5/3) = (5/9)(-3/5) = -1/3
2. Divide 3rd term by 2nd term. (-5/27)÷(5/9)= (-5/27)(9/5) = -1/3
3. Divide 4th term by 3rd term. (5/81)÷(-5/27) = (5/81)(-27/5) = -1/3

All three are the same, so the sequence is geometric,
with r = -1/3.

The correct choice is 1.

Answer 3

so the sum is -1/3?

Answer 4

@wwe123

Answer 5

yes

Answer 6

my online homework says its wrong:(

Answer 7

@DukeShadows

Answer 8

i followed it all and it looked right to me...gosh im sorry

Answer 9

so 1/3 is the right answer? or do i need to do something with 1/3?

Answer 10

i thought i had to do more than just 1/3

Answer 11

assuming thats the correct sequence then itd be right unless you had to plug it in as a function in that case

Answer 12

@thomaster any ideas?

Answer 13

@agent0smith

Answer 14

Hmmm I'm coming up with -5/4 for the answer.
Can you check and see if that's right?

I can try to explain it if it is.
I'm not great with arithmetic and geometric series though :p

Answer 15

its not right:(

Answer 16

Hmmm :c

Answer 17

since |r| < 1, we can use infinite sum formula i think

Answer 18

bahhh i typed it into wolfram wrong!! :3
15/4?

I cheats lol

Answer 19

yay!!!!!!! how did u do it????

Answer 20

I can't remember how to find the common ratio and all that business...
Refer to wwe's notes for that.

I was simply looking at the sequence and tried to write it as a summation.

See how it's alternating?
So we'll have a (-1)^n somewhere in the summation giving us that alternating sign.

And we have powers of 3 in the denominators (starting with 3^0 = 1 for the first term).

\[\Large =\sum_{n=0}^{\infty}(-1)^n\frac{5}{3^n}\]Then from there I cheat and put it into wolfram :c
http://www.wolframalpha.com/input/?i=summation+from+n%3D0+to+n%3Dinfinity+of+%28-1%29%5En+5%2F%283%5En%29

Answer 21

yeah thats the formula i used!! well i probably just worked it out wrong! and how did u put that in wolfram?!?

Answer 22

Click the link, you can see the text I typed into the search box.
You have to use a lot of WORDS to get Wolfram to work correctly.

Answer 23

can you type this into wolfram for me:))) hahaha