Investigation

Dear pupils,

If you have any resources that will help others understand finding patterns, please list them below.


 * __Resources__**

__Rectangle Pattern Challenges__ - [|http://math.rice.edu/~lanius/Lessons/Patterns/rect.html]

To find out the Nth term, there are certain formulae we can use. //Basic Increments// E.g. 1,2,3,4,5,6..... d(n-1)+i n=Term number d=increment(ifference i=initial number //Cumulative Increments// E.g. 1,2,4,7,11,15... d(n-1)+i+c(__n-2)(n-1)__ 2 c=cumulative difference -by lateef

to find out the nth term, and the difference of the given nos. is constant, there is a certain method. Eg.:a,b,c,d,e,f ... (They are algebra symbols.) Steps: do b-a. Eg.:b-a=5 The difference is the number of n's In this eg. it is 5n. If it is negative,like -3, it is -3n. Do the others to find out the bits of the formula.

Lesson to be continued... ... ... ... ... -Rayner


 * __Questions posed by pupils__**

Mdm Teo, is there a method to find the pattern faster?

(Search for 'Arithmetic Progression' on the web to find out more)

Mdm Teo, is there a formula for every pattern?

(If there is a pattern, you can surely find the formula, right?)

I have just found the magic trick about 1's:

1×1= 1 11×11=1 2 1 111×111=12 3 21 1111×1111=123 4 321 11111×11111=1234 5 4321..............................

The middle number (in red)is always the sum of the digits in the multipier, the first and last digits in the product is always 1.

ng jian rong

But be careful. It only ends at 111111111×111111111 The pattern. Rayner

=Then, Mdm Teo, you mentioned that if there's a pattern, there's a formula. What about the Fibonacci sequence? What's the formula? = =Alex = =(Alex, since you have done research on the Fibonacci, do you think there is a formula?) = = = = Mdm Teo, our research does not have anything to do about finding out the formula of Fibonacci numbers. But Alex, ask Jeremy and you will surely find answers as on a Tuesday during lunch, I talked with him and asked him about the formula about the Fibonacci sequence. He said n cubed and blah blah blah. Couldn't remember it, such a long formula. Anyway Mdm Teo, what is the formula for the WS 126 or whatever about the distractions in the movie theater? = =Isaac =

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How am I supposed to draw an even-number-side by an even-number-side magic square Rayner

Answering Isaac question... Put the aisle in the middle. Triangle numbers!!! Rayner

Alex, I can faintly remember, but I think it something to do with rounding off, phi (otherwise known as the golden ratio) and the square root of 5. Rayner