Calculating nth Term of Sequences: What Now?

AI Thread Summary
The discussion revolves around calculating the nth term of two sequences and clarifying a homework question. The first sequence's nth term is identified as -2n + 4, while the second sequence's nth term is 2n - 24. The key question is determining the value of n for which the first sequence's term equals four times the second sequence's term. After clarification, the confusion about the question is resolved. The focus is on solving the equation a_n = 4b_n for n.
BerriesAndCream
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Homework Statement
The nth term of the sequence 2, 0, -2, -4, -6 ... is 4 times the nth term of the sequence -22, -20, -18, -16, -14, ... Work out the value of n.
Relevant Equations
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I don't understand what the question is asking.

the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.
 
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BerriesAndCream said:
Homework Statement:: The nth term of the sequence 2, 0, -2, -4, -6 ... is 4 times the nth term of the sequence -22, -20, -18, -16, -14, ... Work out the value of n.
Relevant Equations:: .

I don't understand what the question is asking.

the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.
If ##a_n = -2n + 4## is the n-th term of the first sequence, and ##b_n = 2n - 24## is the n-th term of the second sequence, what they're asking is this: For which value of n is ##a_n = 4b_n##?
 
Mark44 said:
If ##a_n = -2n + 4## is the n-th term of the first sequence, and ##b_n = 2n - 24## is the n-th term of the second sequence, what they're asking is this: For which value of n is ##a_n = 4b_n##?
oh... all clear now. thank you.
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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