• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4

# 2D &amp; 3D Sequences.

Extracts from this document...

Introduction

2D & 3D Sequences

Plan of Investigation

In this experiment I am going to require the following:

A calculator
A pencil
A pen
Variety of sources of information
Paper
Ruler

In this investigation I have been asked to find out how many squares
would be needed to make up a certain pattern according to its sequence.
The pattern is shown on the front page. In this investigation I
hope to find a formula which could be used to find out the number
of squares needed to build the pattern at any sequencial position.
Firstly I will break the problem down into simple steps to begin
with and go into more detail to explain my solutions. I will illustrate
fully any methods I should use and explain how I applied them to
this certain problem.

Middle

have seen a number of different patterns.

Firstly I can see that the number of squares in each pattern is an odd number.

Secondly I can see that the number of squares in the pattern can
be found out by taking the odd numbers from 1 onwards and adding
them up (according to the sequence). We then take the summation
(å) of these odd numbers and multiply them by two. After doing this
we add on the next consecutive odd number to the doubled total.

I have also noticied something through the drawings I have made
of the patterns. If we look at the symetrical sides of the pattern
and add up the number of squares we achieve a square number.

Conclusion

successful.

Sequence 5:
1. 2(52) - 10 + 1
2. 2(25) - 10 + 1
3. 50 - 10 + 1
4. 50 - 9
5. = 41
Successful

Sequence 6:
1. 2(6
2) - 12 + 1
2. 2(36) - 12 +1
3. 72 - 12 + 1
4. 72 - 11
5. = 61
Successful

Sequence 8:
1. 2(8
2) - 16 + 1
2. 2(64) - 16 + 1
3. 128 - 16 + 1
4. 128 - 15 5. = 113
Successful
The formula I found seems to be successful as I have shown on the
previous page. I will now use the formula to find the number of squares in a higher sequence.

So now I wil use the formula 2n
2 - 2n + 1 to try and find
the number of squares contained in sequence 20.

Sequence 20:

2 (20
2) - 40 + 1
2(400) - 40 + 1
800 - 40 + 1
800 - 49
= 761

Instead of illustrating the pattern I am going to use the method
I used at the start of this piece of coursework. The method in which
Iused to look for any patterns in the sequences. I will use this
to prove the number of squares given by the equation is correct.
As shown below:

2(1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37) + 39 = 761

I feel this proves the equation fully.

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Consecutive Numbers essays

1. ## GCSE Maths Coursework - Maxi Product

7.2x7.8 56.16 15 7.3 and 7.7 7.3+7.7 7.3x7.7 56.21 15 7.4 and 7.6 7.4+7.6 7.4x7.6 56.24 15 7.5 and 7.5 7.5+7.5 7.5x7.5 56.25- Maxi Product 15 7 2/9 and 7 7/9 7 2/9+7 7/9 7 2/9x7 7/9 56.179 (3dp) 15 7 5/9 and 7 4/9 7 5/9+7 4/9 7 5/9x7 4/9 56.247 (3dp)

2. ## Investigate the Maxi Product of numbers

Product of number 12 6 and 6 6+6 6x6 36 13 6.5 and 6.5 6.5+6.5 6.5x6.5 42.25 14 7 and 7 7+7 7x7 49 15 7.5 and 7.5 7.5+7.5 7.5x7.5 56.25 16 8 and 8 8+8 8x8 64 What I notice: I notice that the Maxi product is retrieved when the two halves of the selected number are multiplied together.

1. ## In this investigation I will explore the relationship between a series of straight, non-parallel, ...

But the sequence for Cross-over Points is: COP(1) = 0 COP(2) = 1 COP(3) = 3 COP(4) = 6 COP(5) = 10 COP(6) = 15 COP (2) is not equal to 3 and COP (3) is not equal to 6.

2. ## I am to conduct an investigation involving a number grid.

two numbers is 20 Box 3 56 57 58 61 62 63 66 67 68 [image025.gif] 56 x 68 = 3808 66 x 58 = 3828 3828 - 3808 = 20 The difference between the two numbers is 20 � 4 x 4 Boxes Box 1 5 6 7 8

1. ## Borders and squares

That way I will be able to show my work better. Seq. no 1 2 3 4 5 6 No. Of cubes 1 5 13 25 41 61 x(2n2)

2. ## Analyse the title sequences of two TV programmes, comparing and contrasting the techniques used ...

The viewer is immediately aware of the Metropolitan Police Badge as the camera lingers on this image in a close up and is informed that a gritty slice of a police action drama rather than a fantasy drama is about to begin.

1. ## Investigating a Sequence of Numbers.

6 24 120 720 5040 40320 n! 1 2 6 24 120 720 cn : (n + 2)! - n! 5 22 114 696 4920 39600 T1 = c1 = 1 T2 = c1 + c2 = 5 + 22 = 27 T3 = c1 + c2 + c3 = 5 + 22 + 114 = 141

2. ## Investigate the sequence of squares in a pattern.

2(n2 - 2n + 1) + 2n - 1 3) 2n2 - 4n + 2 + 2n - 1 4) 2n2 - 2n + 1 Therefore my final equation is: 2n2 - 2n + 1 Proving My Equation and Using it to Find the Number of Squares in Higher Sequences I can deduct from this

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to