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.
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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.