SOLUTION: Please help with this question: each term of a sequence is determined by adding half to the preceding term.The sum of the first twenty five terms of the sequence equals the square

Question 841898: Please help with this question: each term of a sequence is determined by adding half to the preceding term.The sum of the first twenty five terms of the sequence equals the square of the twenty fifth term.Calculate the possible values of the first term
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
each term of a sequence is determined by adding half to the preceding term.The sum of the first twenty five terms of the sequence equals the square of the twenty fifth term.Calculate the possible values of the first term
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1st term: x
2nd term: x + 1/2
3rd term: x + 2(1/2)
....
....
25th term: x + 24(1/2)
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Sum:: S(25) = (25/2)(x + x+12)
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Equation:
12.5(2x+12) = (x+12)^2
25(2x+12) = 2(x^2+24x+144)
50x + 300 = 2x^2 + 48x + 288
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2x^2 - 2x - 12 = 0
x^2 - x - 6 = 0
(x-3)(x+2) = 0
x = 3 or x = -2
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Cheers,
Stan H.
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