the sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen of the sequence is -165 find the 18th term of the sequence?
(10/2)(2a + 9d) = -60
2a + 9d = -12
(15/2)(2a + 14d) = -165
2a + 14d = -22
subtract them: 5d = -10 ---> d = -2
in 2a + 9d = -12
2a - 18 = -12
a = 3
now that you know that a=3 and d=-2
find term(18) = a + 17d = .....
-31
i dont understand
i dont understand the question
please use another method
Why did the linear sequence go to a therapist? Because it couldn't find its sum of purpose!
Now, to solve your problem, let's use a "sumful" approach. The sum of the first ten terms of the sequence is -60, and the sum of the first fifteen terms is -165. That means the difference between the sums of ten terms and fifteen terms is -165 - (-60), which simplifies to -165 + 60 = -105.
Since we're given the sum of ten terms, let's find the average value of each term by dividing -105 by 5 (the difference in the number of terms): -105 ÷ 5 = -21.
Now, we can find the 18th term by multiplying the average value by the number of terms: -21 × (18 - 10) = -21 × 8 = -168.
So, the 18th term of the sequence is -168. Keep those linear jokes in line!
To find the 18th term of the sequence, let's first find the common difference of the linear sequence.
The sum of the first ten terms of the sequence is given as -60. We can use the formula for the sum of an arithmetic series:
Sn = (n/2)(2a + (n-1)d),
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Plugging in the given values, we have:
-60 = (10/2)(2a + (10-1)d),
-60 = 5(2a + 9d),
-12 = 2a + 9d. [Equation 1]
Similarly, the sum of the first fifteen terms of the sequence is given as -165:
-165 = (15/2)(2a + (15-1)d),
-165 = 7.5(2a + 14d),
-22 = 2a + 14d. [Equation 2]
Now, we have a system of two equations with two variables (a and d). We can solve this system of equations to find the values of a and d.
Subtracting Equation 2 from Equation 1, we get:
(-12) - (-22) = (2a + 9d) - (2a + 14d),
10 = -5d,
d = -2.
Substituting d = -2 in Equation 1, we find:
-12 = 2a + 9(-2),
-12 = 2a - 18,
6 = 2a,
a = 3.
Therefore, the first term (a) of the sequence is 3, and the common difference (d) is -2.
To find the 18th term of the sequence, we can use the formula for the nth term of an arithmetic sequence:
an = a + (n-1)d,
where an is the nth term, a is the first term, and d is the common difference.
Plugging in the values, we have:
a18 = 3 + (18-1)(-2),
a18 = 3 + 17(-2),
a18 = 3 - 34,
a18 = -31.
Therefore, the 18th term of the sequence is -31.