anonymous
  • anonymous
find a formula for the general term of the sequence. -3/2, -1/6, 1/12, 3/20
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Alright. so the best way to analze this sequence is to look at a sequence for the numerator, call it \(a_n\), make a sequence for the denominator, call it \(b_n\), then call the whole sequence \[t_n=\frac{a_n}{b_n}\]
anonymous
  • anonymous
So lets look at all the numerators. You have the sequence \(\{-3,-1,1,3\}\). Now this has a interesting pattern but you notice that it starts at \(-3\) and increases by \(2\) right? And ill be right over @vk278
anonymous
  • anonymous
yes

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anonymous
  • anonymous
So then in general, for a sequence starting at c and increasing by d, the formula is: \[t_n=c+(n-1)d\]
anonymous
  • anonymous
yup
anonymous
  • anonymous
So we can write the numerator sequence as \[a_n=(-3)+(n-1)(2)=-3+2n-2=2n-5\] Ok?
anonymous
  • anonymous
oh thanks
anonymous
  • anonymous
the denominator would be?
anonymous
  • anonymous
Goot question. Let's look at the denominator. The denominator has the sequence \(\{2,6,12,20\}\)...So...wait just a second.
anonymous
  • anonymous
ok
anonymous
  • anonymous
What patterns do you see?
anonymous
  • anonymous
ummmm
anonymous
  • anonymous
increasing
anonymous
  • anonymous
Haha that's true! Um I see that it is increasing by \((2n)\)
anonymous
  • anonymous
So like the first one is increasing by 2, the second by 4, the next by 6, the next by 8 right?
anonymous
  • anonymous
According to wolframalpha.com, a plausible pattern for the Equation is \[b_n=n^2-n\] Which works right?
anonymous
  • anonymous
Err im sorry \[b_n=n^2+n\]
anonymous
  • anonymous
yes thank you
anonymous
  • anonymous
what did you type in to wolfarama to gt the answer
anonymous
  • anonymous
wolfamalpha

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