the basic formula for arithmetic sequence is a(n) = a(1) + (n-1) * d
the basic formula for arithmetic series is s(n) = ((a(1) + a(n))/2) * n
given s(3) = 15 and s(7) = 63. plugging in all of the known quantities into s(7) - s(3) gives
a(7) - a(3) = 8. plugging all values into this gives 4 * d = 8 or d = 2.
given s(3) = (a(1) + a(2) + a(3)) = 3 * a(1) + 3 * d = 3 * a(1) + 6 = 15 or a(1) = 3.
with a(1) = 3 and d = 2, we can get a(20) = a(1) + 19 * d = 3 + 38 = 41.
given a(1) and a(20), we can get s(20) = ((3 + 41)/2)*20 = 22 * 20 = 440.
