The problem is: 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.