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Created: May 19, 2015

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### 4 Reviews

- Owen1348668 months agoreport
This rich task from the legendary Mr Barton will really spark students interest. Starting with linear sequences, students form a pair of simultaneous equations and solve them. What happens if they start with 2 different sequences? Try it yourself and see if your curiosity isn't piqued!

Can you explain what you have discovered?

How would you convince someone it always works?

How would you explain why it works?

The other way around: If a pair of equations has a solution of x = -1, y = 2, does it mean they are in a sequence?

Can you make up pairs of equations that have solutions:

x = 1, y = -2

x = -1, y = -2

x = 1, y = 2

What other questions might a mathematician ask?

Can you explain what you have discovered?

How would you convince someone it always works?

How would you explain why it works?

What happens if you try linear sequences that descend?

Are there any linear sequences that don’t have solutions? Why is this?

What happens if you have subtractions?

What happens if you use negative numbers, decimals or fractions?

What happens if you use another type of sequence?

What happens if one of the equations is linear and the other a quadratic?

What other questions might a mathematician ask?

Ideas for other sequences to try:

Descending linear

Fibonacci

Geometric

Pascal’s Triangle

3D (x, y and z)