Although the intended answer here is \(C\), you should know that there is no correct answer to this. I could easily say the answer is \(B\).

You can ask me why. Well, my explanation is: the \(n ^{th}\) term of this sequence is \(f(n)\) where \[f(n)=-\frac{n^5-15n^4+85n^3-213n^2+262n-720}{24}.\]Plug in \(n=1, 2, 3, 4, 5\) and get \(f(n)= 25, 24, 22, 19, 15\) [your sequence]. Plug in \(n=6\) and you'll get \(f(n)=5\). So, \(B\) is a perfectly valid answer.

I know that this is not the answer you want and you're probably getting angry at me right now! What I'm trying to say is there's no correct answer.

@Iitian Singh
–
Tushar's many accounts have been banned. Please in the future email me at discussions@brilliant.org to report cheating. I deleted the comment because, I thought it distracted from the point Mursalin was trying to make.

The \(n^{th}\) term of this series is \(A_{n}=A_{n-1}-n\) where \(25\) is the \(0th\) term; hence the \(5^{th}\) term which is what your looking for is \(A_{5}=A_{4}-5\). Therefore \(A_{5}=15-5\) which is \(10\) hence the answer is \(C\).

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TopNewestAlthough the intended answer here is \(C\), you should know that there is no

correctanswer to this. I could easily say the answer is \(B\).You can ask me why. Well, my explanation is: the \(n ^{th}\) term of this sequence is \(f(n)\) where \[f(n)=-\frac{n^5-15n^4+85n^3-213n^2+262n-720}{24}.\]Plug in \(n=1, 2, 3, 4, 5\) and get \(f(n)= 25, 24, 22, 19, 15\) [your sequence]. Plug in \(n=6\) and you'll get \(f(n)=5\). So, \(B\) is a perfectly valid answer.

I know that this is not the answer you want and you're probably getting angry at me right now! What I'm trying to say is there's no

correctanswer.Alt text

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Comment deleted Sep 24, 2013

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What second solution? Are you referring to the comment I posted in reply to Tushar?

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How did u get this f(n)

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why was that comment deleted i wrote in it that tushar is a cheater who cheats from many id's and has atleast 20 ids on brillaint

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I used Lagrange interpolation. But this is not the only way.

For example: you could add \((n-1)(n-2)(n-3)(n-4)(n-5)\) to the polynomial to get a different value for the sixth term.

This way you can practically get anything (even complex numbers) for the sixth term!

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10

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10

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10, because 25-1=24, 24-2=22,22-3=19,19-4=15, so 15-5=10

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The \(n^{th}\) term of this series is \(A_{n}=A_{n-1}-n\) where \(25\) is the \(0th\) term; hence the \(5^{th}\) term which is what your looking for is \(A_{5}=A_{4}-5\). Therefore \(A_{5}=15-5\) which is \(10\) hence the answer is \(C\).

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Well, It is necessary to ask you what part of Mathematics is it after we will conclude an answer.

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C,10

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we can do this in this way to: here consecutive nos are being subtracted.i from 25 then 2 from 24 and then 3 from 22 and so on..........

so the ultimate answer is 15-5(as it is the 5th term in sequence)=10 (c)

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10

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c

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It's C. 10

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