SOLUTION: The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is -165. Find the 18th term of the sequence.

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Question 1118102: The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence
is -165. Find the 18th term of the sequence.
Found 3 solutions by stanbon, MathTherapy, ikleyn:
Answer by stanbon(75887)   (Show Source):
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The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is -165 find the 18th term of the sequence.
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10(a(1)+a(10))/2 = -60
15(a(1)+a(15))/2 = -165
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a(1)+a(10) = -12
a(1)+a(15) = -22
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a(10)-a(15) = 10
5d = 10
d = 2
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a(1) + 9d = -12
a(1) + 18 = -12
a(1) = -30
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Ans:: a(18) = -30 + 17*2 = -16
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Cheers,
Stan H.
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Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website!

The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is -165 find the 18th term of the sequence

Correct answer:

Answer by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website!
The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is -165 find the 18th term of the sequence.
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        The solution by @stanbon contained errors.
        I fixed the errors and put the rectified solution below.

10(a(1)+a(10))/2 = -60
15(a(1)+a(15))/2 = -165
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a(1)+a(10) = -12
a(1)+a(15) = -22
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a(10)-a(15) = 10
-5d = 10
d = -2
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a(1) + a(10) = -12
a(1) + (a(1) + 9d) = -12
2a(1) - 18 = -12
2a(1) = 6
a(1) = 3
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Ans:: a(18) = 3 + 17*(-2) = 3 - 34 = -31.