Number Sequences

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Task: My tasks are too:

1) Find the product of the top left number and the bottom right

number in this box.

2) Do the same with the top right and bottom left numbers.

3) Calculate the difference between these products.

1) I will firstly calculate the product of the top left number and the

bottom right number:

12 x 23 = 276

I will then do the same with top right and bottom left numbers:

13 x 22 = 286

I will now calculate the difference between these two numbers:

286_

276

10

2) I will now investigate further, by doing the next set of numbers:

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I will now calculate the product of the top left number and the bottom

right number:

13 x 24 = 312

I will then do the same with top right and bottom left numbers:

14 x 23 = 322

I will now calculate the difference between these two numbers:

322_

312

10

3) I will now do the next set of numbers:

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I will now calculate the product of the top left number and the bottom

right number:

14 x 25 = 350

I will then do the same with top right and bottom left numbers:

15 x 24 = 360

I will now calculate the difference between these two numbers:

360_

350

10

4) I will now do the next set of numbers:

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I will now calculate the product of the top left number and the bottom

right number:

15 x 26 = 390

I will then do the same with top right and bottom left numbers:

16 x 25 = 400

I will now calculate the difference between these two numbers:

400_

390

10

5) I will now put the results into a table and do an analysis of the

data to see if there are any patterns. Then I can make a prediction

for the next set of results:

Product of the top left number and the bottom right number:

The difference between each answer:

Product of the top right number and bottom left number:

The difference between each answer:

The difference between these two numbers:

First set of numbers:

12 x 23 = 276

312_

276

36

13 x 22 = 286

322_

286

36

286_

276

10

Second set of numbers:

13 x 24 = 312

350_

312

38

14 x 23 = 322

360_

322

38

322_

312

10

Third set of numbers:

14 x 25 = 350

390_

350

40

15 x 24 = 360

400_

360

40

360_

350

10

Fourth set of numbers:

15 x 26 = 390

16 x 25 = 400

400_

390

10

6) I have found a pattern. This is what the patterns look like:

276 312 350 390

[image001.gif] [image001.gif] [image001.gif]

36 38 40

[image002.gif] [image002.gif]

2 2

286 322 360 400

[image001.gif] [image001.gif] [image001.gif]

36 38 40

[image002.gif] [image002.gif]

2 2

The second sets of numbers are the differences between the numbers on

the first row. On the third row, these numbers are the differences
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between the differences. There fore with this pattern I can predict

what the next two sets of numbers are going to be:

Product of the top left number and the bottom right number:

Product of the top right number and bottom left number:

The difference between these two numbers

Fifth set of numbers:

390 + 42 = 432

400 + 42 = 442

442_

432

10

Sixth set of numbers:

432 + 44 = 476

442 + 44 = 486

486_

476

...

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