# arithmetic

Which number should come next in this series?

25,24,22,19,15

A. 4 B. 5 C. 10 D. 14

Note by Pryhant Kielh
4 years, 9 months ago

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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.

Alt text

- 4 years, 9 months ago

Comment deleted Sep 24, 2013

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

- 4 years, 9 months ago

How did u get this f(n)

- 4 years, 9 months ago

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

- 4 years, 9 months ago

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.

Staff - 4 years, 9 months ago

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!

- 4 years, 9 months ago

10

- 2 years, 10 months ago

10

- 3 years, 5 months ago

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

- 3 years, 8 months ago

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 $$C$$.

- 4 years, 9 months ago

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

- 4 years, 9 months ago

C,10

- 4 years, 9 months ago

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)

- 4 years, 9 months ago

10

- 4 years, 9 months ago

c

- 4 years, 9 months ago

It's C. 10

- 4 years, 9 months ago