# Next number in the pattern?

#### Leonidas

I took this stupid quiz on finding the next number in the pattern, and at the end, it didn't tell me the right answers!!!

the one that stumped me was: 73, 61, 56. 62, ?

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#### Vatican Hell

My only guess after skimming at it would be 39...that would fit in the pattern so far...but I don't know if it's right. Every other number subtracts 17, while the other opposite set would add 1 each time....but that's probably wrong.

#### quasar987

Homework Helper
Gold Member
I think the goal is to find the general term $a_n$ of the sequence.

#### Data

well just giving you 4 terms doesn't tell you anything about the general form. 39 is as good an answer as any. Obviously you can make the rest of the terms whatever you want. What sort of quiz was this? Silly questions As for whether it's part of a well-known sequence of interest, the online integer sequence encyclopedia gives no results.

#### Office_Shredder

Staff Emeritus
Gold Member
First it decreases by 12, then 5, then increases by 1. So the change in the increase/decrease goes:
6, 5. My guess is the increase would increase by 4, meaning the next term would be 5 greater, or 67

But there's no obvious pattern involved, because the second and third term are part of a decreasing sequence, but the fourth term is greater than the third

#### StatusX

Homework Helper
I agree, it doesn't seem like there is enough information. You could always fit a polynomial to the points (1,73),( 2,61), etc, and extend the series that way (which is essentially what you're doing when you look at the difference between the difference between ... between the difference of consecutive terms (see the method of differences used in Babbages' http://en.wikipedia.org/wiki/Difference_engine" [Broken]) ). What is the context of the problem? Give some more examples from this problem set. Should we look at mathematical properties like the prime factorizations or sums of digits, or could it be something like the number of days in certain months of the year?

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54 ;)

#### micromass

My guess is 0, since it is the only other root of the polynomial

$$x(x-73)(x-61)(x-56)(x-62)$$

But seriously, this is silly. Only giving 4 terms is not enough to deduce a pattern. But I think the guess of Vatican Hell is the best you can make...

#### MANU MOP

You're exaggerating! ;)
It wasn't so hard
73: (7-3) x3 ...

#### Slats18

Gotta agree with Manu Mop here. Given integer ab, where a,b are part of the counting integers 0 to 9, the next number is ab-((a-b)*b)

73-((7-3)*3)=61
61-((6-1)*1)=56
56-((5-6)*6)=62
62-((6-2)*2)=54

Bit obscure, but it fits...

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