Math Stinger # 130
by Steve Edwards, Professor of Mathematics

A list of numbers is in arithmetic progression if the difference
between adjacent numbers is the same for each adjacent pair. 
So 15, 20, 25, 30   and 7, 10, 13, 16
are two lists that are in arithmetic progression. 
Consider all lines given by equations Ax + By + C = 0,
where A, B, C  is a list of numbers in arithmetic progression.
What can you say about the graphs of these lines?

 

These lines all pass through the point (1, -2).

If A, B, and C are in arithmetic progression, then 2B = A + C, or A - 2B + C = 0.

Comparing this with the general equation of the straight line,

1A - 2B + C = 0

Ax + By + C = 0

That means the point (x,y) = (1,-2) always will be a solution to these equations.

 

Solutions to this Stinger were submitted by Sameer Parvez, whose solution is used above,  and Jonathan Phillips  

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