Question
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
Answers
Reiny
As usual, let the first term be a, and we know d = .5
S<sub>25</sub> = 25/2[2a + 24(.5)] = 25a + 150
T<sub>25</sub> = a + 24d = a + 12
given: S<sub>25</sub> = (T<sub>25</sub>)^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
S<sub>25</sub> = 25/2[2a + 24(.5)] = 25a + 150
T<sub>25</sub> = a + 24d = a + 12
given: S<sub>25</sub> = (T<sub>25</sub>)^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