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S = an^2 + bn

Where a and b are constants.

Possible values for S are: 6, 15, 27, 42 and 60

Possible values for n are: 1 when S=6, 2 when S=15, 3 when S=27, 4 when S=42 and 5, when S=60.

I am asked to find the values of a and b.

The way I tried to tackle it was sort it out into quadratic form:

an^2 + bn - s = 0

I then substituted suitable values for n and s. After that, I rearrange the equation so I can get the value of of either b or a and try to solve it using simultaneous equations.

I've tried many times to find the values of a or b but everytime I end up with a 0 = 0 scenario and in the case of S=60 and n=5:

0(5^2) + 0(5) - 60 does not equal 0.

My other idea is to use quadratic formula somehow to find the coefficients of n^2 and n but I can't find anything about solving it this way.

I would appreciate it if somebody with a good sturdy brain could please help a dumb richard like myself.

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# Help a Lost Soul

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