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 870008: 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
Answer by mananth(16946) About Me  (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
S10=-60
S15=-165
S18=?
Sn = %28n%2F2%29%282a%2B%28n-1%29d%29
S10-%2810%2F2%29%282a%2B9d%29
-60= 10a+45d..............(1)
S15 = (15/2)(2a+14d)
-165=(15/2)(2a+14d)
-330 =30a+210d.............(2)
d= common difference
a= first term

45 d + 10 a = -60 .............1
Total value
210 d + 30 a = -330 .............2
Eliminate y
multiply (1)by -3
Multiply (2) by 1
-135 d -30 a = 180
210 d + 30 a = -330
Add the two equations
75 d = -150
/ 75
d = -2.00
plug value of d in (1)
45 d + 10 a = -60
-90 + 10 a = -60
10 a = -60 + 90
10 a = 30
a = 3
d= -2 common difference
a= 3 first term
m.ananth@hotmail.ca