I'm so confused on this, I'm not sure what I'm supposed to use for any of this, I don't know the common denominator or anything.
Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1.
http://imgur.com/BaADfyq

- sloppycanada

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- ganeshie8

start with \(-4\), and keep multiplying by \(5\) to get the next term.

- sloppycanada

So T6 is -62,500?

- ganeshie8

first term, \(\large t_1 ~=~-4\)
second term, \(\large t_2 ~=~-4*5 = -20\)
third term, \(\large t_3 ~=~-20*5 = -100\)
keep going till the 6th term

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## More answers

- ganeshie8

-62,500 is wrong

- sloppycanada

Sorry, I did too many of them. -2500.

- ganeshie8

show me the work instead

- sloppycanada

T4 = -100 x 5 = -500
T5 = -500 x 5 = -2500
T6 = -2500 x 5 = -12500

- ganeshie8

Good!

- sloppycanada

And then how do I go about finding the sum of an infinite series?

- ganeshie8

look at the terms :
\[-4,~~-20,~~-100,~~-500,~~-2500,~~ \ldots\]
what do you notice ? do they seem to converge to some number ?

- sloppycanada

You could go on for ever without getting a sum.

- ganeshie8

Yes, so we say the "sequence doesn't converge" and the infinite sum doesn't exist

- sloppycanada

So for an equation like this - Find the sum of the infinite series 3 + 1.2 + 0.48 + 0.192 + ...if it exists.
All I would do is use the formula to find the equation of the infinite series?

- ganeshie8

what kind of series is it, geometric/arithmetic ?

- sloppycanada

Geometric?

- ganeshie8

there is a nice criterion for testing convergence of geometric series, you simply look at the common ratio

- ganeshie8

whats the common ratio of given series ?

- sloppycanada

The equation is tn/(tn-1)

- sloppycanada

Common ratio is 2.5

- ganeshie8

yes work it
common ratio = (next term)/(present term)

- ganeshie8

looks you have worked it in reverse : (present term)/(next term)

- ganeshie8

try again

- sloppycanada

.4?

- ganeshie8

yes common ratio = 0.4 which is between -1 and 1
so the given series conveges

- ganeshie8

A geometric series converges if the common ratio is between -1 and 1

- ganeshie8

use infinite sum formula to find the sum

- ganeshie8

do you have the formula wid u ?

- sloppycanada

S(infinite) = 3/t-.4

- sloppycanada

I have it in my notes

- ganeshie8

\[\large S_{\infty} ~=~\dfrac{t_1}{1-r}\]

- ganeshie8

\[\large S_{\infty} ~=~\dfrac{3}{1-0.4}\]

- ganeshie8

simplify

- sloppycanada

5?

- ganeshie8

Yes!

- sloppycanada

I have three more if you have time?

- ganeshie8

okay il try, post

- sloppycanada

http://gyazo.com/f47f214fcdb2adb56c90ca6794e3f48d

- ganeshie8

Firs test if the series converges by finding the common ratio

- ganeshie8

whats the common ratio ?

- sloppycanada

1.33?

- ganeshie8

Yes, which is "not" in between -1 and 1
so the series does not converge.

- ganeshie8

we say the sum does not exist

- sloppycanada

Okay so the answer would be "No solution"

- ganeshie8

As you can see, the common ratio decides whether an infinite converges to some number, or if it diverges

- ganeshie8

Answer would be "does not converge"

- sloppycanada

If it converges then it has a sum, if it does not converge there is not really a solution?

- ganeshie8

yes, do you see why the common ratio of 1.33 gives a diverging sum ?

- sloppycanada

Because it's larger then 1? and not between that -1 and 1

- ganeshie8

Yes, when you multiply the first term by 1.33, you get a bigger next term; the terms keep growing and the sum wont reach a specific number

- sloppycanada

So for this problem - http://gyazo.com/15138c898cca305ec43a79e298d55821
The answer would be .498

- ganeshie8

how did u get 0.498 ?

- ganeshie8

im asking because im getting a more nice looking number : 0.5

- sloppycanada

I didn't round.

- ganeshie8

me neither
could you show ur work please

- sloppycanada

\[S \infty = \frac{ 1 }{ 3 }\div 1-.33\]

- ganeshie8

Ahh okay, you're rounding 1/3 to 0.33

- ganeshie8

i worked it like this :
\[\large S_{\infty}~=~\dfrac{1/3}{1-1/3} = \dfrac{1}{3-1}=\dfrac{1}{2}=0.5\]

- sloppycanada

I'm not sure why I changed from a fraction to a decimal. Fractions are more precise aren't they?

- ganeshie8

Yep
Fractions are exact
decimals are not so exact when you get a repeating decimal

- ganeshie8

1/2 = 0.5
both are exact

- ganeshie8

1/3 = 0.33333333333333333333333333...
clearly the decimal wont be exact because you can't write out infinitely many 3's

- sloppycanada

Okay, last one - http://gyazo.com/50d340d91d94093d361677d900fa46ee
Answer is 1.

- ganeshie8

\[\huge \color{red}{\checkmark}\]

- sloppycanada

Ah hah! Thank you!

- sloppycanada

Not sure how to show my appreciation on this site (if there are points or something), but let me know if there is.

- ganeshie8

yw! click the "Best Response" button next to any reply if you find the answer helpful

- ganeshie8

you could also write a testimonial if you think the helper is amazing

- ganeshie8

not encouraging you to write a testimonial for me right now, but just letting you know :)

- sloppycanada

Finding the sum of an geometric Find S12 for the series 1 + 2 + 4 + 8 +... like this is 49,140

- ganeshie8

go through this when u have time to know more about the site
http://openstudy.com/code-of-conduct

- ganeshie8

how did u get 49.140 ?

- sloppycanada

Sorry it should be 8,190.
2((1-2^12)/(1-2)) = 8190

- sloppycanada

|dw:1435126030016:dw|

- ganeshie8

why are you multiplying by 2 ?

- ganeshie8

first term is 1 right

- ganeshie8

|dw:1435126092819:dw|

- sloppycanada

Okay so it'd just be 4095

- ganeshie8

Correct.

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