anonymous
  • anonymous
I need help on my Arithmetic and Geometric Sequence worksheet -24,-8,-2 2/3, -8/9 8,-4,2,-1 3/4,-1/2,1/3,-2/9 Find the next three terms
Algebra
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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whpalmer4
  • whpalmer4
Okay, do you know what an arithmetic sequence is, and a geometric sequence?
anonymous
  • anonymous
Arithmetic is subtracting? Geometric is multiplying
whpalmer4
  • whpalmer4
arithmetic is adding or subtracting, yes, and geometric is multiplying (or dividing) An arithmetic sequence always has the same difference between two adjacent terms, and a geometric sequence always has the same quotient between two adjacent terms. So are these arithmetic or geometric sequences?

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anonymous
  • anonymous
Geometric sequence?
whpalmer4
  • whpalmer4
Yes, all 3 are geometric sequences. Can you work out what the ratio is for the first one? \[-24,-8,-2\frac{2}{3},-\frac{8}{9}\]
whpalmer4
  • whpalmer4
\[\frac{-24}{-8}=\]\[\frac{-8}{-2\frac{2}{3}}=\]\[\frac{-2\frac{2}{3}}{-\frac{8}{9}}=\]
anonymous
  • anonymous
They all equal to 3
whpalmer4
  • whpalmer4
Each number in the sequence is 1/3 of the previous one, isn't it? \[-24*\frac{1}{3} = -8\]\[-8*\frac{1}{3}=-\frac{8}{3} \ (=-2\frac{2}{3})\]\[-\frac{8}{3}*\frac{1}{3} = -\frac{8}{9}\]
whpalmer4
  • whpalmer4
so what is the term after \(-\dfrac{8}{9}\) going to be?
anonymous
  • anonymous
-8/27
whpalmer4
  • whpalmer4
that's right! Here are the first 10 terms of that sequence: \[\left\{-24,-8,-\frac{8}{3},-\frac{8}{9},-\frac{8}{27},-\frac{8}{81},-\frac{8}{243},-\frac{8}{729},-\frac{8}{2187},-\frac{8}{6561}\right\}\]
whpalmer4
  • whpalmer4
Now how about the next problem? \[8,-4,2,-1\] What is the common ratio between the terms?
anonymous
  • anonymous
Well the pattern is positive, negative, positive, negative. But the ratio is ... I don't know
anonymous
  • anonymous
Is it -2?
whpalmer4
  • whpalmer4
\[\frac{8}{-4} = -2\]\[\frac{-4}{2} = -2\]\[\frac{2}{-1} = -2\] Looks like we divide by \(-2\) to get the next term...
whpalmer4
  • whpalmer4
That makes the next term in the sequence = ???
anonymous
  • anonymous
So the next 3 terms would be .5 , -.25, .125
whpalmer4
  • whpalmer4
Yep. Probably a bit clearer if you keep them as fractions rather than decimals. \[8,-4,2,-1,1/2,-1/4,1/8\]
whpalmer4
  • whpalmer4
How about the last problem?
anonymous
  • anonymous
\[\frac{ 3 }{ 4 } ,-\frac{ 1 }{ 2 },\frac{ 1 }{ 3 },-\frac{ 2 }{ 9 }\]
whpalmer4
  • whpalmer4
Looking back at the problem, it's a little bit ambiguous as to whether we need to find the next term in each sequence, or the next 3 terms in each sequence. Probably safer to do the next 3 terms!
anonymous
  • anonymous
I got it!!! its \[\frac{ 1 }{ 1 }\] thats how i find the next 3 terms?
anonymous
  • anonymous
Nevermind
anonymous
  • anonymous
I'm stuck on the last one
whpalmer4
  • whpalmer4
\[\frac{3}{4}*\frac{a}{b} = -\frac{1}{2}\] can you find a fraction that makes that work?
whpalmer4
  • whpalmer4
don't worry about the negative sign, you can just put that on afterward \[\frac{3}{4}*\frac{a}{b} = \frac{1}{2}\] maybe start by multiplying everything by 4 \[4*\frac{3}{4}*\frac{a}{b} = 4*\frac{1}{2}\]\[3*\frac{a}{b} = 2\]\[\frac{a}{b} = \frac{2}{3}\] so we get the next term by multiplying by \(-\dfrac{2}{3}\) Let's check that: we start with \frac{3}{4}: \[\frac{3}{4}*-\frac{2}{3} = -\frac{3*2}{4*3} = -\frac{1}{2}\checkmark\] \[-\frac{1}{2}*-\frac{2}{3} = \frac{1*2}{2*3} = \frac{1}{3}\checkmark\] looks like that is the right multiplier...
anonymous
  • anonymous
Yesss
anonymous
  • anonymous
Thank you for helping me!! :)
whpalmer4
  • whpalmer4
Hopefully these will all be easy for you now! As I mentioned earlier, you might want to play it safe and figure out the next 3 terms for each of the sequences. If it turns out you didn't need to, well, you got some practice.
anonymous
  • anonymous
True that

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