Next Number | 5 Sep 2009

Kshiteej's Avatar, Join Date: Jul 2009
Contributor
Which is the next number in below series.

1, 2, 7, 12, 19, 42, ?
0
shabbir's Avatar, Join Date: Jul 2004
Go4Expert Founder
Looks like we would have OP as winner.
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xpi0t0s's Avatar, Join Date: Aug 2004
Mentor
Nothing found here:
http://www.research.att.com/~njas/se...lish&go=Search

Without commas this returns 432 pages of results; looked through the first few but there was nothing obvious.

So we need more terms to deduce the sequence.

Of course, any number can be the answer, for example 99, because these are the roots of the equation
x^7-182*x^6+10500*x^5-252586*x^4+2762303*x^3-13306896*x^2+24059196*x-13272336
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SaswatPadhi's Avatar, Join Date: May 2009
~ Б0ЯИ Τ0 С0δЭ ~
Quote:
Originally Posted by xpi0t0s View Post
Nothing found here:
http://www.research.att.com/~njas/sequences/?q=1%2C2%2C7%2C12%2C19%2C42&sort=0&fmt=0&language= english&go=Search

Without commas this returns 432 pages of results; looked through the first few but there was nothing obvious.

So we need more terms to deduce the sequence.
Even I searched there, in vain

Quote:
Originally Posted by xpi0t0s View Post
Of course, any number can be the answer, for example 99, because these are the roots of the equation
x^7-182*x^6+10500*x^5-252586*x^4+2762303*x^3-13306896*x^2+24059196*x-13272336
Yeah, but then how do we express the general term, say 'n'th term of the series ??
As you already said, we probably need some more terms ...
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shabbir's Avatar, Join Date: Jul 2004
Go4Expert Founder
Kshiteej can we have the answer of this so we can have the question for today.
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xpi0t0s's Avatar, Join Date: Aug 2004
Mentor
Assuming that is enough to deduce the series, then using the same technique as before I get 113.
Code:
1					
2	1				
7	5	4			
12	5	0	-4		
19	7	2	2	6	
42	23	16	14	12	6

113	71	48	32	18	6
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Seema786's Avatar
Banned
that was nice xpi0t0s
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neo_vi's Avatar, Join Date: Feb 2008
Invasive contributor
The next number is 37. Am i right?
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Kshiteej's Avatar, Join Date: Jul 2009
Contributor
Hi all,
sorry for my late reply.
Consider alternative terms set 2 ie 2,12,42
12-2 = 10 = (2)^3 + 2
42-12 = 30 = (3)^3 + 3

Consider alternative terms set 1 ie. 1,7,19
7-1 = 6 = (2)^2 + 2
19-7= 12 = (3)^2 + 3

as the next number belongs to alternative set 1 ( because next numbers postion is odd)

next number should be 19 + (4)^2 + 4 = 39


So the answer is 39.
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neo_vi's Avatar, Join Date: Feb 2008
Invasive contributor
I too thought in the same angle. But some thing went wrong

1, 2, 7, 12, 19, 42

The diff b/w 1st and third is 6 (7-1)

The diff b/w 5th and 3rd is 12 (19-7)

So,The diff b/w 7th and 5th should be 18 (37-19) which follows multiples of 6.

Similarly,
the diff b/w 4th and 2nd is 10 (12-2)

the diff b/w 6th and 4th is 30 (42-12)