Homework Help: arithmetic

Posted by Anonymous on Sunday, February 21, 2010 at 4:42am.

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

arithmetic - Reiny, Sunday, February 21, 2010 at 7:36am
As usual, let the first term be a, and we know d = .5

S₂₅ = 25/2[2a + 24(.5)] = 25a + 150

T₂₅ = a + 24d = a + 12

given: S₂₅ = (T₂₅)^2

25a + 150 = (a+12)^2
a^2 + 24a + 144 = 25a + 150
a^2 - a - 6 = 0
(a-3)(a+2) = 0

a = 3 or a = -2

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