Find the number of terms of the Arithmetic progression 4+6.5+9+11.5+... needed to make a total of 126
a = 4, d = 2.5, n = ?? , sum(n) = 126
(n/2)(8 + 2.5(n-1)) = 126
n(8 + 2.5n - 2.5) = 252
2.5n^2 + 5.5n - 252 = 0
5n^2 + 11n - 504 = 0
using the formula, I got n = 9 or n = a negative
of course n has to be a whole number.
sum(9) = (9/2)(8 + 8(2.5)) = 126
so 9 terms