sloppycanada
  • sloppycanada
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
start with \(-4\), and keep multiplying by \(5\) to get the next term.
sloppycanada
  • sloppycanada
So T6 is -62,500?
ganeshie8
  • 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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ganeshie8
  • ganeshie8
-62,500 is wrong
sloppycanada
  • sloppycanada
Sorry, I did too many of them. -2500.
ganeshie8
  • ganeshie8
show me the work instead
sloppycanada
  • sloppycanada
T4 = -100 x 5 = -500 T5 = -500 x 5 = -2500 T6 = -2500 x 5 = -12500
ganeshie8
  • ganeshie8
Good!
sloppycanada
  • sloppycanada
And then how do I go about finding the sum of an infinite series?
ganeshie8
  • ganeshie8
look at the terms : \[-4,~~-20,~~-100,~~-500,~~-2500,~~ \ldots\] what do you notice ? do they seem to converge to some number ?
sloppycanada
  • sloppycanada
You could go on for ever without getting a sum.
ganeshie8
  • ganeshie8
Yes, so we say the "sequence doesn't converge" and the infinite sum doesn't exist
sloppycanada
  • 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
  • ganeshie8
what kind of series is it, geometric/arithmetic ?
sloppycanada
  • sloppycanada
Geometric?
ganeshie8
  • ganeshie8
there is a nice criterion for testing convergence of geometric series, you simply look at the common ratio
ganeshie8
  • ganeshie8
whats the common ratio of given series ?
sloppycanada
  • sloppycanada
The equation is tn/(tn-1)
sloppycanada
  • sloppycanada
Common ratio is 2.5
ganeshie8
  • ganeshie8
yes work it common ratio = (next term)/(present term)
ganeshie8
  • ganeshie8
looks you have worked it in reverse : (present term)/(next term)
ganeshie8
  • ganeshie8
try again
sloppycanada
  • sloppycanada
.4?
ganeshie8
  • ganeshie8
yes common ratio = 0.4 which is between -1 and 1 so the given series conveges
ganeshie8
  • ganeshie8
A geometric series converges if the common ratio is between -1 and 1
ganeshie8
  • ganeshie8
use infinite sum formula to find the sum
ganeshie8
  • ganeshie8
do you have the formula wid u ?
sloppycanada
  • sloppycanada
S(infinite) = 3/t-.4
sloppycanada
  • sloppycanada
I have it in my notes
ganeshie8
  • ganeshie8
\[\large S_{\infty} ~=~\dfrac{t_1}{1-r}\]
ganeshie8
  • ganeshie8
\[\large S_{\infty} ~=~\dfrac{3}{1-0.4}\]
ganeshie8
  • ganeshie8
simplify
sloppycanada
  • sloppycanada
5?
ganeshie8
  • ganeshie8
Yes!
sloppycanada
  • sloppycanada
I have three more if you have time?
ganeshie8
  • ganeshie8
okay il try, post
sloppycanada
  • sloppycanada
http://gyazo.com/f47f214fcdb2adb56c90ca6794e3f48d
ganeshie8
  • ganeshie8
Firs test if the series converges by finding the common ratio
ganeshie8
  • ganeshie8
whats the common ratio ?
sloppycanada
  • sloppycanada
1.33?
ganeshie8
  • ganeshie8
Yes, which is "not" in between -1 and 1 so the series does not converge.
ganeshie8
  • ganeshie8
we say the sum does not exist
sloppycanada
  • sloppycanada
Okay so the answer would be "No solution"
ganeshie8
  • ganeshie8
As you can see, the common ratio decides whether an infinite converges to some number, or if it diverges
ganeshie8
  • ganeshie8
Answer would be "does not converge"
sloppycanada
  • sloppycanada
If it converges then it has a sum, if it does not converge there is not really a solution?
ganeshie8
  • ganeshie8
yes, do you see why the common ratio of 1.33 gives a diverging sum ?
sloppycanada
  • sloppycanada
Because it's larger then 1? and not between that -1 and 1
ganeshie8
  • 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
  • sloppycanada
So for this problem - http://gyazo.com/15138c898cca305ec43a79e298d55821 The answer would be .498
ganeshie8
  • ganeshie8
how did u get 0.498 ?
ganeshie8
  • ganeshie8
im asking because im getting a more nice looking number : 0.5
sloppycanada
  • sloppycanada
I didn't round.
ganeshie8
  • ganeshie8
me neither could you show ur work please
sloppycanada
  • sloppycanada
\[S \infty = \frac{ 1 }{ 3 }\div 1-.33\]
ganeshie8
  • ganeshie8
Ahh okay, you're rounding 1/3 to 0.33
ganeshie8
  • 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
  • sloppycanada
I'm not sure why I changed from a fraction to a decimal. Fractions are more precise aren't they?
ganeshie8
  • ganeshie8
Yep Fractions are exact decimals are not so exact when you get a repeating decimal
ganeshie8
  • ganeshie8
1/2 = 0.5 both are exact
ganeshie8
  • ganeshie8
1/3 = 0.33333333333333333333333333... clearly the decimal wont be exact because you can't write out infinitely many 3's
sloppycanada
  • sloppycanada
Okay, last one - http://gyazo.com/50d340d91d94093d361677d900fa46ee Answer is 1.
ganeshie8
  • ganeshie8
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sloppycanada
  • sloppycanada
Ah hah! Thank you!
sloppycanada
  • 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
  • ganeshie8
yw! click the "Best Response" button next to any reply if you find the answer helpful
ganeshie8
  • ganeshie8
you could also write a testimonial if you think the helper is amazing
ganeshie8
  • ganeshie8
not encouraging you to write a testimonial for me right now, but just letting you know :)
sloppycanada
  • sloppycanada
Finding the sum of an geometric Find S12 for the series 1 + 2 + 4 + 8 +... like this is 49,140
ganeshie8
  • ganeshie8
go through this when u have time to know more about the site http://openstudy.com/code-of-conduct
ganeshie8
  • ganeshie8
how did u get 49.140 ?
sloppycanada
  • sloppycanada
Sorry it should be 8,190. 2((1-2^12)/(1-2)) = 8190
sloppycanada
  • sloppycanada
|dw:1435126030016:dw|
ganeshie8
  • ganeshie8
why are you multiplying by 2 ?
ganeshie8
  • ganeshie8
first term is 1 right
ganeshie8
  • ganeshie8
|dw:1435126092819:dw|
sloppycanada
  • sloppycanada
Okay so it'd just be 4095
ganeshie8
  • ganeshie8
Correct.

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