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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

start with \(-4\), and keep multiplying by \(5\) to get the next term.
So T6 is -62,500?
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

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question