24 57

25 62

The pattern in this table is for the T- Number it is plus one every time and for the T-Total it is plus five every time.

The nth term = 5N – 63

To find the nth tern I looked at the T – Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 63.

Prediction

I predict that when the t - number is 27 the T – total will be 72, and also in an equation the T –number will be 28 and the T-Total will be 77 this is shown in the table below.

26 x 5 – 63 = 67

27 x 5 – 63 = 72

28 x 5 – 63 = 77

T-Number T-Total

18 34

19 39

20 44

21 49

The pattern in these tables is plus one every time in the T – Number and for the T – Total it is plus five very time.

The nth term = 5N – 56

To find the nth tern I looked at the T – Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 56.

Prediction

I predict that when the t - number is 23 the T – total will be 59, and also in an equation the T –number will be 24 and the T-Total will be 64 this is shown in the table below.

22 x 5 – 56 = 54

23 x 5 – 56 = 59

24 x 5 – 56 = 64

T-Number T-Total

16 31

17 36

18 41

19 46

The pattern with this table is for the T number if plus one every time and for the T total it is plus five every time.

The nth term = 5N – 49

To find the nth tern I looked at the T – Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 49.

Prediction

I predict that when the t - number is 21 the T – total will be 56, and also in an equation the T –number will be 22 and the T-Total will be 61 this is shown in the table below.

20 x 5 – 49 = 51

21 x 5 – 49 = 56

22 x 5 – 49 = 61

T – Number T – Total

14 28

15 33

16 38

The pattern for this table is for the T number is plus one and for the T total is plus five.

The nth term = 5N – 42

To find the nth tern I looked at the T – Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 56.

Prediction

I predict that when the t - number is 18 the T – total will be 48, and also in an equation the T –number will be 19 and the T-Total will be 53 this is shown in the table below.

17 x 5 – 42 = 43

18 x 5 – 42 = 48

19 x 5 – 42 = 53

Formulas

3 x 3 = 19 + (5 x (r-8)

8 x 8 = 34 + (5 x (r–18)

9 x 9 = 37 + (5 x (r – 22)

10 x 10 = 40 + (5 x (r-22)

11 x 11 = 43 + (5x (r-24)

12 x 12 = 46 + (5 x (r-26)

These grids are to work out certain sizes; if you want to work out any size grin you can use the formula below.

(19 + 3 x (r – 3) + (5 x *t – 2 x (T + 1)

What I found out

In this investigation I have found out that this formula above will work out the sizes for any size grid.