... cubes 1 5 13 25 41 61 85 113 I am going to use this next method to see if I can work out some sort of pattern: Sequence Calculations Answer 1 =1 1 2 2(1)+3 5 3 2(1+3)+5 13 4 2(1+3+5)+7 25 5 2(1+3+5+7)+9 41 6 2(1+3+5+7+9)+11 ...

... + c = 0 0.5 - 0.5 + c = 0 c = 0 an + bn + c 0.5n2 - 0.5n I have now found a formula which can be used to work out the number of switches required for any ...

... third column is based on the number of tens the squared numbers have. So for example, digits 0-9 have no tens inside them. But digits 10-19, all of these numbers have one ten inside them. e.g. T U ...

... is the sth perfect square and the tth triangular number, i.e. N=s2=Tt. So N=N(s,t), or s=s(N) and t=t(N), where . Here I list the s and t parameters for the first five triangular squares: 1. s=1, t=1. t/s=1. 36. s=6, t=8. t/s=1.333... 1225. s=35, t=49. t/s=1.4. 41616. s=204, t=288. t/s=1.411764705... 1413721. s=1189, t=1681. t/s=1.413793103... I also listed the ratio t(N)/s(N) for each of these N. ...

... Bill' and 'NYPD Blue' are the two television title sequences to be compared. As both programmes are crime related dramas, it will be interesting to investigate whether both title sequences create similar expectations of the proceeding programme. The title sequence ...

... to get the perimeter. E.g. Perimeter = shortest +middle + longest length 5 + 12 + 13 = 30 units 7 + 24 + 25 = 56 units I found the area for the sequences 5, 12, 13 and 7, ...

... we look at the table and take the furthest column to the right and work our way the left, we see that: 2 to the power of 0 is = 1 2 to the power of 1 is = 2 (2x1 ...

... and from there we will be able to find the formula. I also predict that in this project we will get the formula (2n2) - 2n+1. Now I am going to draw the diagrams: 1 2 3 4 5 6 I have achieved ...

... 4x4 shape = 25 squares 5x5 shape = 41 squares 6x6 shape = 61 squares I now have enough data to analyse my results: Number in sequence (n) Total number of squares (tn) 1 1 2 5 3 13 4 25 5 41 6 61 To work out which formula to use I will now put ...

... the 5th is N+4. This gives you 5N+10 5N+10 = 15,20,25,30,35 etc. Every fifth number.> If the 1st number is N, the 2nd is N+1, the 3rd is N+2, the 4th is N+3, the 5th is N+4, the 6th is N+5. ...

... show that it works with algebra. X, X+1, X+2 1st *3rd = X*(x+2) = X2=2X 2nd squared = (X+1)2 = (X+1)(X+1) (X +1)(X+1) = X2 + 1 + 1X + 1X = X2 + 2X + 1 The only difference is +1. It ...

... show that it works with algebra. X, X+1, X+2 1st *3rd = X*(x+2) = X2=2X 2nd squared = (X+1)2 = (X+1)(X+1) (X +1)(X+1) = X2 + 1 + 1X + 1X = X2 + 2X + 1 The only difference is +1. It ...

... there is an equal gap each time. The more consecutive numbers the bigger the gap between each sum. E.g. 2 Consecutive Numbers I noticed that all of these consecutive numbers are all odd numbers 3,5,7,9,11.I also noticed that an Nth term could be ...

... there is an equal gap each time. The more consecutive numbers the bigger the gap between each sum. E.g. 2 Consecutive Numbers I noticed that all of these consecutive numbers are all odd numbers 3,5,7,9,11.I also noticed that an Nth term could be ...

... there is an equal gap each time. The more consecutive numbers the bigger the gap between each sum. E.g. 2 Consecutive Numbers I noticed that all of these consecutive numbers are all odd numbers 3,5,7,9,11.I also noticed that an Nth term could be ...

... all the values up to that term. For example, the 200th term can be found but we would have to find all the values up to the 199th term. This is time-consuming and instead of having to do this, we ...

... they are world- devouring vampires. This made such atrocities 'easier' to commit as an image of a world- devouring vampire is being put into their heads, instead of normal human beings. The picture of a railway straight track going directly ...

... be to prove that he can get from one step to an other formally put P (k) ? P (k +1). If we can show this than it follows that man can get from the first to the second step, ...

... to see if I can work out some sort of pattern: Sequence Calculations Answer 1 =1 1 2 2(1)+3 5 3 2(1+3)+5 13 4 2(1+3+5)+7 25 5 2(1+3+5+7)+9 41 6 2(1+3+5+7+9)+11 61 7 2(1+3+5+7+9+11)+13 85 8 2(1+3+5+7+9+11+13)+15 113 9 2(1+3+5+7+9+11+13+15) +17 145 What I am doing above is shown with the ...

... a constant difference of 2 I believed that the formula would include n². I applied this to the first number in the sequence '2'. So n² = (1 x 1 = 1). To get the first number of the sequence ...

... individual rules for these three sectors of numbers, I will then work out the general rule for any amount of numbers it can be split into. For example, it can be split up into five numbers and I will be ...

... that we use to buy our daily needs to knowing how to count. Whenever humans encounter numbers in magazines they tend to believein them. Any quantitative instrument is believed in todays society because it is known that most of the ...

... c we will have to put the formula into action: If n = 1 U1 = 1* - 1 + c and because u = 1 c must be +1 so the formula must be Un = n* - n + 1 ...

... 91 92 [image004.gif] 81 x 92 = 7452 91 x 82 = 7462 7462 - 7452 = 10 The difference between the two numbers is 10 Box 3 69 70 79 80 [image005.gif] 69 x 80 = 5520 79 x ...

... and before that there were two 0's and before that there was one 0, so I estimate that there will eventually be nine 0's and the number will be finally 1.000000000. Investigation 1:carried on 1.000152588 1.000076294 1.000038147 1.000019074 1.00009537 ...