Remember Pascal's triangle?
your coefficents are 1,30,375
So, your a=6, then n=6 (last row) and verify by a^2*15=375 yes, you are correct.
The first 3 terms of (1 + ax)^n
= 1 + n(ax) + n(n-1)/2(a^2x^2) + ...
so nax = 30x
na = 30
a = 30/n
n(n-1)/2(a^2x^2) = 375x^2
n(n-1)(900/n^2) = 750
900(n-1) - 750n
n = 5
then a = 30/5 = 6
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