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anonymous
 one year ago
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
anonymous
 one year ago
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

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whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1Okay, do you know what an arithmetic sequence is, and a geometric sequence?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Arithmetic is subtracting? Geometric is multiplying

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1arithmetic 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?

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1Yes, 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
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{24}{8}=\]\[\frac{8}{2\frac{2}{3}}=\]\[\frac{2\frac{2}{3}}{\frac{8}{9}}=\]

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1Each 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
 one year ago
Best ResponseYou've already chosen the best response.1so what is the term after \(\dfrac{8}{9}\) going to be?

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1that'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
 one year ago
Best ResponseYou've already chosen the best response.1Now how about the next problem? \[8,4,2,1\] What is the common ratio between the terms?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well the pattern is positive, negative, positive, negative. But the ratio is ... I don't know

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{8}{4} = 2\]\[\frac{4}{2} = 2\]\[\frac{2}{1} = 2\] Looks like we divide by \(2\) to get the next term...

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1That makes the next term in the sequence = ???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the next 3 terms would be .5 , .25, .125

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1Yep. Probably a bit clearer if you keep them as fractions rather than decimals. \[8,4,2,1,1/2,1/4,1/8\]

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1How about the last problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 3 }{ 4 } ,\frac{ 1 }{ 2 },\frac{ 1 }{ 3 },\frac{ 2 }{ 9 }\]

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1Looking 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
 one year ago
Best ResponseYou've already chosen the best response.0I got it!!! its \[\frac{ 1 }{ 1 }\] thats how i find the next 3 terms?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm stuck on the last one

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{3}{4}*\frac{a}{b} = \frac{1}{2}\] can you find a fraction that makes that work?

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1don'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
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for helping me!! :)

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1Hopefully 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.
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