What is the next term of the given sequence...

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Discussion Overview

The discussion revolves around identifying the next term in a numerical sequence that appears to be related to perfect squares. Participants explore various interpretations of the sequence, including the reversal of digits in square numbers.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the sequence consists of perfect squares with their digits reversed, leading to the next term being 982.
  • Others question the validity of this interpretation and seek clarification on how the next term was derived.
  • One participant introduces Lagrange interpolation, arguing that without a specified polynomial degree, any finite sequence can be generated by multiple formulas.
  • Another participant presents a different mathematical problem involving the division of a circle into areas based on the number of points, indicating a shift in focus from the original sequence discussion.
  • Some participants express uncertainty about the reasoning behind the proposed next term and share their thought processes regarding the sequence.

Areas of Agreement / Disagreement

There is no consensus on the next term of the sequence, as participants present competing interpretations and reasoning. Some agree on the reversal of digits in square numbers, while others challenge this approach or introduce unrelated mathematical concepts.

Contextual Notes

Participants express varying levels of understanding regarding the sequence, with some relying on intuition and others on formal mathematical reasoning. The discussion includes references to external resources and previous posts that may influence interpretations.

Who May Find This Useful

This discussion may be of interest to individuals exploring numerical sequences, mathematical reasoning, or those interested in the interplay between different mathematical concepts.

Aladin
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What is the next term of the given sequence..
1,4,9,61,52, 63, 94, 46, 18, 001, 121, 441, 961, 691, 522, 652, ...(?)
 
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Is the tenth term supposed to be 001?
 
Yes, and Aladin just fixed it. Anyhow, each term simply represents perfect squares with digits reversed; thus the next term is 172 with digits reversed (i.e., 982). This thread probably belongs in h*ttp://www.physicsforums.com/forumdisplay.php?f=33[/color]
 
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Yes it is supposed to be 001! What is happening is that you are finding the square numbers and reversing the order of digits! So the next number would be 982.

Piece of cake...
 
haha, nice one mtanti!
 
according to the lagrange interpolation theore, any finite number of n numbers can be the first n elements of a sequence defiuned by a polynomial of degree at most n-1, so there is no way to guess the formula for a given sequence unless you specify that the formula is a polynomial of degree at most n-1.


e.g. the sequence 2,4,6,8, is obtained not just from the formula a(n) = 2n, for n=1,2,3,4, but also from the formula a(n) =

2(x-2)(x-3)(x-4)(x-5)/(1-2)(1-3)(1-4)(1-5)

+ 4(x-1)(x-3)(x-4)(x-5)/(2-1)(2-3)(2-4)(2-5)

+6(x-1)(x-2)(x-4)(x-5)/(3-1)(3-2)(3-4)(3-5)

+8(x-1)(x-2)(x-3)(x-5)/(4-1)(4-2)(4-3)(4-5)

+11(x-1)(x-2)(x-3)(x-4).

but this foprmula gives a(5) = 11, instead of 10.

so what is lagrange's IQ?
 
And what does guessing what answer you wanted have to do with IQ?

Here's an easier one: If you mark the circumference of a circle with n points, NOT equally spaced, and draw all lines connecting them, you divide the face of the circle into areas (the purpose of "NOT equally spaced" is that no more than 2 lines cross at a point so you get the maximum possible number of areas). With 1 point, one area; 2 points, 2 areas; 3 points, 4 areas; 5 points, 8 areas; 9 points, 16 areas. How many areas do you get with 6 points? (there is a simple formula.)
 
Aladin said:
What is the next term of the given sequence..
1,4,9,61,52, 63, 94, 46, 18, 001, 121, 441, 961, 691, 522, 652, ...(?)

http://www.research.att.com/~njas/sequences/A002942

HallsofIvy said:
Here's an easier one: If you mark the circumference of a circle with n points, NOT equally spaced, and draw all lines connecting them, you divide the face of the circle into areas (the purpose of "NOT equally spaced" is that no more than 2 lines cross at a point so you get the maximum possible number of areas). With 1 point, one area; 2 points, 2 areas; 3 points, 4 areas; 5 points, 8 areas; 9 points, 16 areas. How many areas do you get with 6 points? (there is a simple formula.)

http://www.research.att.com/~njas/sequences/A000127
 
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Mtanti ! are you sure that the next term is 982.If it is right then how did you find this ?please tell me.
 
  • #10
IQ test: i am a 64 yer old math prof, with brown hair, and arthritis. i like to blog on physics forums and read comic books. my favorite wines include lescours "L", beychevelle, terrabianca campaccio, and ? [what wine am i thinking of?]

and what is your IQ?
 
  • #11
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  • #12
ans

982 must b.squares in reverse
 
  • #13
bomba923 said:
Probably read my https://www.physicsforums.com/showpost.php?p=1071552&postcount=3, posted here about an hour before mtanti's post :rolleyes: (remember to highlight my post to read it!)

Hey! I had no idea about that! At first I thought about squares with modulo arithmetic as it was evident that it involved squares from the first few terms. Then I started seeing 61 and 18 and I started suspecting the reverse thing... So I tried it myself on my calculator and started revealing the sequence!
 
  • #14
mtanti said:
Hey! I had no idea about that!
uhh sure...

And neither did (about three days later[/size])
the_next_einstein said:
982 must b.squares in reverse
:rolleyes:
 
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  • #15
mathwonk said:
IQ test: i am a 64 yer old math prof, with brown hair, and arthritis. i like to blog on physics forums and read comic books. my favorite wines include lescours "L", beychevelle, terrabianca campaccio, and ? [what wine am i thinking of?]

and what is your IQ?

Ha trick question. The answer is beer!
 

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