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Please help... Only 2 days left for me on a summer school class and I am lost...
1. What is the sum of the geometric sequence 8, 16, 32 . if there are 15 terms? (1 point)
2. What is the sum of the geometric sequence 4, 12, 36 . if there are 9 terms? (1 point)
3. What is the sum of a 6term geometric sequence if the first term is 11, the last term is 11,264 and the common ratio is 4? (1 point)
4. What is the sum of an 8term geometric sequence if the first term is 10 and the last term is
781,250? (1 point)
Show all work as well
 8 months ago
 8 months ago
Please help... Only 2 days left for me on a summer school class and I am lost... 1. What is the sum of the geometric sequence 8, 16, 32 . if there are 15 terms? (1 point) 2. What is the sum of the geometric sequence 4, 12, 36 . if there are 9 terms? (1 point) 3. What is the sum of a 6term geometric sequence if the first term is 11, the last term is 11,264 and the common ratio is 4? (1 point) 4. What is the sum of an 8term geometric sequence if the first term is 10 and the last term is 781,250? (1 point) Show all work as well
 8 months ago
 8 months ago

This Question is Closed

cwrw238Best ResponseYou've already chosen the best response.1
the formula for sum of n terms is Sn = a1 * (1  r^n)  1  r
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
http://www.mathsisfun.com/algebra/sequencessumsgeometric.html
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
But what do I plug in there to get the answers?
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
The link I posted will walk you through what geometric sequences are, and that formula to get the answers!
 8 months ago

cwrw238Best ResponseYou've already chosen the best response.1
r = common ratio = second term / first term a1 = first term and n = number of terms
 8 months ago

cwrw238Best ResponseYou've already chosen the best response.1
so for question 1 r = 16/8 = 2 a1 = 8 and n = 15
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
So would the answer for the first one be 87384?
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
@kathert I agree with 87384 :)
 8 months ago

cwrw238Best ResponseYou've already chosen the best response.1
8 * ( 1  (2)^15)  = 87384 1  (2)
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Oh yay! I got it right! Sorry I suck at math...
 8 months ago

cwrw238Best ResponseYou've already chosen the best response.1
A GS can be written as a, ar , ar^2 , ar^3 .......
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
I've \(always\) been slow at math. But it took practice, and getting help, and I can do more math things now! Best of luck in your class! :) And it looks like you're in good hands with cwrw238 .
 8 months ago

cwrw238Best ResponseYou've already chosen the best response.1
for the last probem you can find the common ratio r by dividing the 8th term by the first then you take the 7th root 8th term = ar^7 8th term / first term = ar^7 / a = r^7 781,250 / 10 = 78125 now use your calculator to find the 7th root of 78125 then use the sum formula gotta go now
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Whoa how do I do 7 root in my calculator??
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Do it like this: r ^ ( 7)
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
That's what you want, \[\Huge r^{\frac{1}{7}}\]
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Haha okay gimme a minute to figure this out...
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
I got 39364 for number 2 is that right?
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Okay okay how do i do the last two??
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
That's what I got for #2 as well.
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
3. What is the sum of a 6term geometric sequence if the first term is 11, the last term is 11,264 and the common ratio is 4? (1 point) Well, the first term is your \(a\).\[a=11\]The last term is your \(a\ r^n\).\[a\ r^n=11,264\]The common ratio is your \(r\).\[r=4\] You need \(\Large a\frac{1r^n}{1r}\).
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
So, you have \(a\) and \(r\), and you need \(n\) or \(r^n\).
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Do you see how to get that?
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
uhhh.... no not really...so it would be 11 (1(4^n)/(14)?
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Yep! Hey, you know \(a\ r^n=11,264\), so you can solve for \(r^n\)! That's how you'll finish that problem.
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
General guideline: if you want something, solve for it.
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
wait so n is 11,246??
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
No, \(a\ r^n=11,264\). So you divide both sides by \(a=11\). That's algebra!
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
im sorry but im so lost.... where does the 11246 come in? do i set it equal to the equation?
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
It is necessary to find the \(r^n\). Let me show you. Are you familiar with algebra? \[a\ r^n = 11,264\]and\[a=11\]By substituting \(11\) for \(a\), which is okay because it's the same value either way, you'll get:\[11\ r^n=11,264\]Now, you want to get \(r^n\) alone. So what you do is, you divide both sides by \(11\). 1. If the two sides are equal, and you do the same thing to both sides, both sides will still be equal! 2. Why divide by \(11\)? Well \(r^n\) is being multiplied by \(11\), and so you want to negate that. You want to make it be \(\Large \frac{\cancel{11}\ r^n}{\cancel{11}}\) So, we left our equation off at\[11\ r^n=11,264\]We divide by \(11\) to get\[\frac{11\ r^n}{11}=\frac{11,264}{11}\]\[\frac{\cancel{11}\ r^n}{\cancel{11}}=\frac{11,264}{11}\]\[r^n=\frac{11,264}{11}\]
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Since you now have \(r^n\), \(a\), and \(r\), you can use that formula that you used for #1 and #2.
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Ohhhhh okay! I get it now!
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
SWEET! :) So, we'll both calculate #3 and see what we get....
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
I got \(2255\)... Let me use Wolfram Alpha to double check. Then I can show you a link to the math.
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=11*%281%2811264%2F11%29%29%2F%281%284%29%29
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Maybe you just had some calculator error.
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Oh I see what I did wrong
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
How would I go about starting the last one?
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Well, I'm sure you know the formula you need to use, by now!\[\text{sum}=a\frac{(1r^n)}{(1r)}\] 4. What is the sum of an 8term geometric sequence if the first term is 10 and the last term is 781,250? (1 point) You need \(a\), \(r\), and \(r^n\), or \(n\). What do you know from the problem, about the geometric sequence?
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Refresher: \(a\) is the first term, or the common multiplier. \(r\) is the common ratio. \(n\) is the number of terms in the sequence.
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
8term \(\rightarrow n=8\) first term is 10 \(\rightarrow a=10\) last term is 781,250 \(\rightarrow a\ r^{n1} =781,250\)
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
so would it be 10 (1(781250/10))/1r?
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Its alright I disappeared for dinner so... haha
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Nope, sorry! Small mistake! \[a\ r^{n1} =781,250\]\(\qquad\Downarrow\qquad\)Substitute \(8\) for \(n\) \[a\ r^{81} =a\ r^{7}=781,250\]\(\qquad\Downarrow\qquad\)Divide both sides by \(a\), and then substitute \(10\) in for \(a\) \[r^7=\frac{781,250}{a}=\frac{781,250}{10}=78,125\]\(\qquad\Downarrow\qquad\)Get the seventh root of both sides\[\sqrt[7]{r^7}=r=\sqrt[7]{78,125}=5\]
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Well, you knew you didn't know \(r\), so I guess your only mistake was substituting \(r^n\) with \(r^{n1}=781,250\), but you definitely had the right idea otherwise! I just found \(r\) for you, then... Any questions on that part? Now you have \(a\), \(n\), and \(r\).
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Which you can rearrange to spell \(r\ a\ n\): fun fact..
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
so it would be 8 *(178125)/(15) just to be sure nice fun fact btw haha
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Haha, thanks! And check your "\(r^n\)", or \(5^8\).
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
You got \(78125\) from \(r^{n1}\), so I see where that came from :) And, yep! \(390625\).
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
so that goes where i put the 78125
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
It is \(r^n\), after all.
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
and your formula is\[\text{sum}=a\frac{(1r^n)}{(1r)}\]
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
I got 781,248 for my answer
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
I got the same! :) Congrats!
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
Any questions about this problem?
 8 months ago

kathertBest ResponseYou've already chosen the best response.0
Nope I'm good! Thank you for your help!
 8 months ago

theEricBest ResponseYou've already chosen the best response.1
You're welcome! Take care!
 8 months ago
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