arithmetic
posted by Anonymous on .
Each term of a progression is determined by adding 0.5 to the preceding term. the sum of the first 25 terms of the progression equals the square of the 25th term. calculate the possible value(s) of the first term

As usual, let the first term be a, and we know d = .5
S_{25} = 25/2[2a + 24(.5)] = 25a + 150
T_{25} = a + 24d = a + 12
given: S_{25} = (T_{25})^2
25a + 150 = (a+12)^2
a^2 + 24a + 144 = 25a + 150
a^2  a  6 = 0
(a3)(a+2) = 0
a = 3 or a = 2