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

Question 1150834: 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 greenestamps, MathLover1, MathTherapy:
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

Let a = first term
Let d = common difference

10th term: a+9d
15th term: a+14d
18th term: a+17d

Sum of first ten terms: -60 = 10 times average of first and tenth terms

[1]

Sum of first 15 terms: -165 = 15 times average of first and 15th terms
[2]

Subtract [1] from [2] and solve for d; then use that value in either [1] or [2] to solve for a.

Finally, use the values of a and d to find the 18th term.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
linear sequences are sequences where the difference between successive terms is always the same
In General we could write an arithmetic sequence like this:
, , , , ...

The sum of the first terms of an arithmetic sequence use this formula:

where is the first term, the number of terms, and is common difference

given:
The sum of the first ten terms of a linear sequence is ; so, we have
........... ten terms=>

..................eq.1

and the sum of the first fifteen terms of the sequence is
........... 15 terms=>

.................eq.2

from eq.1 and eq.2 we have

find first term:
.................eq.2

find the 18th term of the sequence:
, , and

so, your sequence is:
,,,,,,,,,,,,,,,,,,....

Answer by MathTherapy(10556)   (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

Sum of "n" terms of an A.P.: ------- Substituting 10 for n ------ Substituting - 60 for ------- Substituting 15 for n ------------- Substituting - 165 for 5d = - 10 ------- Subtracting eq (i) from eq (ii) d, or common difference = ------ Substituting - 2 for d in eq (i) To find , we substitute into the formula for a term in an A.P., as follows:

RELATED QUESTIONS
The sum of the first ten terms of a linear sequence is -60 and the sum of the first... (answered by mananth)
The sum of the first ten terms of a linear sequence is -60 and the sum of the first... (answered by stanbon,MathTherapy,ikleyn)
The sum of the first ten terms of a linear sequence is -60 and the sum of the first... (answered by greenestamps)
the 15th term in an arithmetic sequence is 129 and the sum of the first fifteen terms is... (answered by josgarithmetic,greenestamps)
Find the sum of the first twenty terms of the arithmetic sequence given that the tenth... (answered by Fombitz)
if seventh term of geometric sequence is 64 and sum of first ten terms is 1023 then find... (answered by richwmiller)
the fifth term of a geometric sequence is 252 and the common ratio is 0.5 find the first... (answered by josgarithmetic,MathTherapy)
The sum of the first two terms of a geometric sequence is 90. The sum of the sixth and... (answered by htmentor)
Find the sum of the first ten terms of the sequence 128, -64, 32, -16,... (answered by jorel555)