# To see if three horizontal rectangle numbers e.g. &#147;12,13,14&#148; &#150; have the same result when you multiply the middle number by 2 and add the 1st and last number together.

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Introduction

Diagram.1

Case.1:

To see if three horizontal rectangle numbers e.g. “12,13,14” – have the same result when you multiply the middle number by 2 and add the 1st and last number together.

Testing:

Conclusion:

This happens because the mean of the 1st and last number is equal to the middle number i.e.:

### Mean of 12 and 14 = 13

## Middle number = 13

## The next part of the scenario was to multiply the middle number by 2 and plus the 1st and last number together;

Middle

Conclusion:

The original formula (Case.1) also works for Variable.2.

Case.3:

Investigate what happens when Mary draws a rectangle around five numbers.

Testing:

I first tried to see if the formula for Case.1 applied for Case.3:

Conclusion:

The formula for Case.3 also works for rectangles with 5 squares whether it is diagonal, horizontal or vertical.

Case.4

Investigate if the formula also works for any amount of rectangle squares:

Testing:

Conclusion:

After doing the previous scenarios I have realised that

Conclusion

71,73,93,91=

Conclusion:

We found out that it is possible to find out the middle number by finding the sum of the parameter and then dividing it by the parameter (squares on the outside.) Another way of finding the middle number was to take two diagonally opposite corners and divide by 2. This works as it is the same as diagonal rectangles (see case.2)

Formula:

n.b = parameter.

= Sum of parameter.

Error! Not a valid link. = Middle number.

Error! Not a valid link. =

Or

Error! Not a valid link. = Two diagonally opposite corners 2

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers section.

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