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 \(C\).

## Comments

Sort by:

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

Log in to reply

Comment deleted Sep 24, 2013

Log in to reply

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

Log in to reply

How did u get this f(n)

Log in to reply

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

Log in to reply

Log in to reply

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!

Log in to reply

10

Log in to reply

10

Log in to reply

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

Log in to reply

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 \(C\).

Log in to reply

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

Log in to reply

C,10

Log in to reply

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)

Log in to reply

10

Log in to reply

c

Log in to reply

It's C. 10

Log in to reply