• 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
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  21. 21
    21
  22. 22
    22
  23. 23
    23
  24. 24
    24
  25. 25
    25
  26. 26
    26
  • Level: GCSE
  • Subject: Maths
  • Word count: 2408

Consecutive Numbers Investigation

Extracts from this document...

Introduction

James Lucas CONSECUTIVE NUMBERS Problem 1 Gap 1 Take three consecutive numbers; square the middle number, multiply the first by the third number. What do you notice? 2, 3, 4 are consecutive numbers they follow on from each other. The next number is one more than. 2, 3, 4 32 = 3*3 = 9 2*4 = 8 Difference 1 The numbers above are consecutive numbers; the difference between them is one. 18, 19, 20 192 = 19*19 = 361 18*20 = 360 Difference 1 97, 98, 99 982 = 98*98 = 9604 97*99 = 9603 Difference 1 117, 118, 119 1182 = 118*118 = 13924 117*119 = 13923 Difference 1 It appears that it will work every time. I have tried it four times and it works all right so far. I will now try decimals. 1.2, 2.2, 3.2 2.22 = 2.2*2.2 = 4.84 1.2*3.2 = 3.84 Difference 1 10.9, 11.9, 12.9 11.92 = 11.9*11.9 = 141.61 10.9*12.9 = 140.61 Difference 1 It would appear that it works using decimals. I will now try negative numbers. -8, -7, -6 -72 = -7*-7 = 49 -8*-6 = 48 Difference 1 -5, -4, -3 -42 = -4*-4 = +16 -5*-3 = +15 Difference 1 I have found out that it also works with negative numbers. ...read more.

Middle

2.5, 7.5, 12.5 2.5*12.5 = 31.25 7.52 = 7.5*7.5 = 56.25 Difference 25 4.2, 9.2, 14.2 4.2*14.2 = 59.64 9.22 = 9.2*9.2 = 84 64 Difference 25 7.1, 12.1, 17.1 7.1*17.1 = 121.41 12.12 = 12.1*12.1 = 146.41 Difference 25 It would appear that it works using decimals. I will now try negative numbers. -1, 4, 9 -1*9 = -9 42 = 4*4 = 16 Difference 25 -10, -5, 0 -10*0 = 0 -52 = -5*-5 = 25 Difference 25 I have found out that it also works with negative numbers. I will now hope to show that it works with algebra. X, X+5, X+10 X*(X+10)= X2=10X (X+5)2=(X+5)(X+5)= X2 + 10 + 5X + 5X = X2 +10X + 25 The only difference is + 25 This shows that the difference will always be 25. Gap Difference 1 1 2 4 3 9 4 16 5 25 Problem 2 Gap 1 Two consecutive numbers square the first, square the second. What do you notice? 5, 6 52 = 5*5 = 25 62 = 6*6 = 36 Difference 11 7, 8 72 = 7*7 = 49 82 = 8*8 = 64 Difference 15 10, 11 102 = 10*10 = 100 112 = 11*11 = 121 Difference 21 I will now try decimals to see if it works the same. ...read more.

Conclusion

15*15 = 225 202 = 20*20 = 400 Difference 175 40, 45 402 = 40*40 = 1600 452 = 45*45 = 2025 Difference 425 It would appear that it works every time. I have tried it three times and it works all right so far. But this time they is a different pattern. I will now try decimals. 5.7, 10.7 5.72 = 5.7*5.7 = 32.49 10.72 = 10.7*10.7 = 114.49 Difference 82 15.1, 20.1 15.12 = 15.2*15.2 = 228.01 20.12 = 20.1*20.1 = 404.01 Difference 176 42.4, 47.4 42.42 = 42.4*42.4 = 1797.76 47.42 = 47.4*47.4 = 2246.76 Difference 449 It would appear that it works using decimals. I will now try negative numbers. -50, -55 -502 = -50*-50 = 2500 -552 = -55*-55 = 3025 Difference 525 -10, -15 -102 = -10*-10 = 100 -152 = -15*-15 = 225 Difference 125 -22, -27 -222 = -22*-22 = 484 -272 = -27*-27 = 729 Difference 245 I have found out that it also works with negative numbers. I will now hope to show that it works using algebra. X, X+5 X2 (X+5)2 (X+5)2(X+5) X2+5X+5X+25 X2+10X+25 Difference 10X+25 Instead of adding the consecutive numbers together and multiplying by 4 you multiply it by 5. Gap Difference 1 2X+1 2 4X+4 3 6X+9 4 8X+16 5 10X+25 ...read more.

The above preview is unformatted text

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

See related essaysSee related essays

Related GCSE Consecutive Numbers essays

  1. GCSE Maths Coursework - Maxi Product

    I yet have not found a number that is the product of three numbers that leaves a result that is more than 64. I will see in fractional number if I can retrieve a number higher than 64 by multiplying three numbers together.

  2. Maths Investigation - Pile 'em High

    I will try and find a formula and test it to make sure it works. I will use a standard sequence rule and put numbers into it. Firstly I will find a sequence to this structure that I am investigating.

  1. Nth Term Investigation

    the numbers go up in 6's because when each side increases it's length by on an extra symbol is needed on all of the 6 sides. The nth term is n x 6. For the fourth Column ( ) the numbers go up 12 then 24 then 36, every time

  2. Borders - a 2 Dimensional Investigation.

    - 2(4) +1 32 - 8 + 1 =25 My formula is correct for this sequence, but to make sure my formula is accurate, I am now going to prove it using structure. When I look at any of the cross shapes, I see that they can be split up

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

    is correct because there are 14 Open Regions in this diagram, and that is what I predicted. Step 2: I will list the number of cross-over points to investigate the pattern in the second sequence. The number of Cross -Over Points is given by: COP(n)

  2. I'm going to investigate the difference between products on a number grid first I'm ...

    1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 The difference between 205 and 45 is 160 because 205 - 45 = 160. 5 x 41 = 205 1 x 45 = 45 55

  1. I am to conduct an investigation involving a number grid.

    now calculated the 5 x 5 boxes using a 10 x 10 grid and have learned that the number which I predicted was accurate and correct. This determines that the formula that I chose to use was the proper one to do this certain part of the investigation with.

  2. The Towers of Hanoi is an ancient mathematical game. The aim of this coursework ...

    So 32 is multiplied by 0.5 to get 16. Our sequence is: S= 32 + 16 + 8 4 +2 +1 To get the sum of a geometric sequence, we need to multiply by the common ratio (0.5) S = a + ar + ar2 + ar3 +... + arn-1 rS = a + ar + ar2 + ar3 +...

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