• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 3286

Number Sums Investigations

Extracts from this document...

Introduction

1 0+1 2 - 3 1+2 4 - 5 2+3 6 1+2+3 7 3+4 8 - 9 4+5, 2+3+4 10 1+2+3+4 11 5+6 12 3+4+5 13 6+7 14 2+3+4+5 15 7+8, 1+2+3+4+5, 4+5+6 16 - 17 8+9 18 3+4+5+6, 5+6+7 19 9+10 20 2+3+4+5+6 21 10+11, 1+2+3+4+5+6, 6+7+8 22 4+5+6+7 23 11+12 24 7+8+9 25 12+13, 3+4+5+6+7 26 5+6+7+8 27 13+14, 2+3+4+5+6+7, 8+9+10 28 1+2+3+4+5+6+7 29 14+15 30 4+5+6+7+8, 6+7+8+9, 9+10+11 31 15+16 32 - 33 16+17, 3+4+5+6+7+8, 10+11+12 34 7+8+9+10 35 17+18, 2+3+4+5+6+7+8, 5+6+7+8+9 36 11+12+13 37 18+19 38 8+9+10+11 39 19+20, 12+13+14, 4+5+6+7+8+9 40 6+7+8+9+10 41 20+21 42 3+4+5+6+7+8+9, 9+10+11+12, 13+14+15 43 21+22 44 2+3+4+5+6+7+8+9 45 22+23, 1+2+3+4+5+6+7+8+9, 5+6+7+8+9+10, 7+8+9+10+11, 14+15+16 46 10+11+12+13 47 23+24 48 15+16+17 49 24+25, 4+5+6+7+8+9+10 50 8+9+10+11+12, 11+12+13+14 51 25+26, 6+7+8+9+10+11, 16+17+18 52 3+4+5+6+7+8+9+10 53 26+27 54 12+13+14+15, 2+3+4+5+6+7+8+9+10, 17+18+19 55 27+28, 1+2+3+4+5+6+7+8+9+10, 9+10+11+12+13 56 5+6+7+8+9+10+11 57 28+29, 7+8+9+10+11+12, 18+19+20 58 13+14+15+16 59 29+30 60 4+5+6+7+8+9+10+11, 10+11+12+13+14, 19+20+21 61 30+31 62 14+15+16+17 63 31+32, 3+4+5+6+7+8+9+10+11, 6+7+8+9+10+11+12, 8+9+10+11+12+13, 20+21+22 64 - 65 32+33, 2+3+4+5+6+7+8+9+10+11, 11+12+13+14+15 66 15+16+17+18, 1+2+3+4+5+6+7+8+9+10+11, 21+22+23 67 33+34 68 5+6+7+8+9+10+11+12 69 34+35, 9+10+11+12+13+14, 22+23+24 70 16+17+18+19, 12+13+14+15+16, 7+8+9+10+11+12+13 71 35+36 72 4+5+6+7+8+9+10+11+12, 23+24+25 73 36+37 74 17+18+19+20 75 37+38, 3+4+5+6+7+8+9+10+11+12, 10+11+12+13+14+15, 13+14+15+16+17, 24+25+26 76 6+7+8+9+10+11+12+13 77 38+39, 2+3+4+5+6+7+8+9+10+11+12, 8+9+10+11+12+13+14 78 1+2+3+4+5+6+7+8+9+10+11+12, 18+19+20+21, 25+26+27 79 39+40 80 14+15+16+17+18 81 40+41, 5+6+7+8+9+10+11+12+13, 11+12+13+14+15+16, 26+27+28 82 19+20+21+22 83 41+42 ...read more.

Middle

- 2 - 4 - 8 - 16 - 32 - 64 - Equations The equation for two number sums is, n+n+1, which is simplified to 2n+1. E.g. 301=2n+1 -1 -1 300=2n 2 2 n=150 150+151=301 The equation for three number sums is, n+n+1+n+2. This is simplified to 3n+3. E.g. 300=3n+3 -3 -3 297=3n 3 3 n=99 99 + 100 + 101=300 The equation for four number sums is, n+n+1+n+2+n+3, which can be simplified to 4n+6. E.g. 310=4n+6 -6 -6 304=4n 4 4 n=76 76+77+78+79=310 The equation for five number sums is, n+n+1+n+2+n+3+n+4. This can be simplified to just 5n+10. E.g. 310=5n+10 -10 -10 300=5n 5 5 n=60 60+61+62+63+64=310 The equation for six number sums is, n+n+1+n+2+n+3+n+4+n+5. This can be simplified to just 6n+15. E.g. 315=6n+15 -15 -15 300=6n 6 6 n=50 50+51+52+53+54+55=315 The equation for seven number sums is, n+n+1+n+2+n+3+n+4+n+5+n+6. This can be simplified to just 7n+21. E.g. 350=7n+21 -21 -21 329=7n 7 7 n=47 47+48+49+50+51+52+53=350 The equation for eight number sums is, n+n+1+n+2+n+3+n+4+n+5+n+6+n+7. This can be simplified to just 8n+28. E.g. 316=8n+28 -28 -28 288=8n 8 8 n=36 36+37+38+39+40+41+42+43=316 The equation for nine number sums is, n+n+1+n+2+n+3+n+4+n+5+n+6+n+7+n+8. This can be simplified to just 9n+36. E.g. 360=9n+36 -36 -36 324=9n 9 9 n=36 36+37+38+39+40+41+42+43+44=360 The equation for 10 number sums is, n+n+1+n+2+n+3+n+4+n+5+n+6+n+7+n+8+n+9. ...read more.

Conclusion

The three number sums all give an answer that is a multiple of three. The four number sums all give an answer that is an even number. Numbers made using five number sums are all multiples of five. Six number sums have answers that all go up in six's For the seven number sums the answers all go up in multiples of seven. In the eight number sums the answers all go up in eights. The answers are all even numbers. Numbers made using nine number sums are all multiples of nine. The ten number sums all give an answer that goes up in tens each time. They are all even numbers as well as being multiples of five. The numbers all end in five. The eleven number sums all give the answer that is a multiple of eleven. Numbers made using twelve number sums go up in twelve's each time, but are not multiples of twelve. They are all even numbers. For the thirteen number sums the number made is always a multiple of thirteen. For all the odd number tables, i.e. 3,5,7 etc, the numbers made are multiples of the number of that table. E.g. for five number sums the numbers go up; 15, 20, 25, 30, etc. For the even numbers the numbers just go up by the number of table, but are not multiples. E.g. for six number sums the numbers go up; 28(+6),35(+6), 42, etc. ...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

    (4.3,4.4,4.3)= 13 --> 4.3+4.4+4.3 --> 4.3x4.4x4.3=81.356 I will now move onto fractional numbers as there can be no other decimal number that can give a result higher than 81.356 using three numbers. I will see in fractional numbers if I can get a number higher than 81.356 from three fractional numbers.

  2. Investigate the Maxi Product of numbers

    which is the highest possible answer which is retrieved when two numbers added together equal 14 are multiplied. 15 (1,14)= 15 à 1+14 à 1x14=14 (2,13)= 15 à 2+13 à 2x13=26 (3,12)= 15 à 3+12 à 3x12=36 (4,11)= 15 à 4+11 à 4x11=44 (5,10)= 15 à 5+10 à 5x10=50 (6,9)=

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

    Some definitions: If (n) is the number of lines (where n can be any natural number) then the number of Open Regions is given by: OR(n) the number of Cross -Over Points is given by: COP(n) the number of Closed Regions is given by: CR(n)

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

    3 65 66 70 71 [image021.gif] 65 x 71 = 4615 70 x 66 = 4620 4620 - 4615 = 5 The difference between the two numbers is 5 � 3 x 3 Boxes Box 1 2 3 4 X X+1 X+2 7 8 9 X+5 X+6 X+7 12 13

  1. Study the topic of trios and work on from that, to discover patterns and ...

    I then had to work out which number factorial to put down. I discovered, by looking at the lower number on the formula for trios, that it is 2 factorial and that the lower number on quartets is 3 factorial.

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

    from the table will be 32 as this is the number of times disc A moves. Ratio - r - This is the amount that a is multiplied to get the next term. So 32 is multiplied by 0.5 to get 16.

  1. Investigate calendars, and look for any patterns.

    by 7, which gives: 7 14 21 28 35 This is 4 more than required each time, so subtract 4 to correct the sequence. Therefore, the expression is: n = 7n - 4 I decided to test my expression on some other columns in the calendar.

  2. To investigate consecutive sums. Try to find a pattern, devise a formulae and establish ...

    9+10+11=30 3n 3x10=30 25+26+27=78 3n 3x26=78 0 + 1 + 2 = 3 1 + 2 + 3 = 6 2 + 3 + 4 = 9 3 + 4 + 5 = 12 4 + 5 + 6 = 15 5 + 6 + 7 = 18 6 +

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