# 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.

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