If the sum of the 4th term and the 7th term is 45.The sum of the 9th term is 117.Find the term when the sum of it is 600
"The sum of the 9th term is 117" makes no sense.
Do you mean : the sum of the first 9 terms is 117
or
The 9th term is 117 ?
104
To find the term when the sum of it is 600, we need to determine the pattern or rule that relates the term number to the corresponding sum.
Let's start by finding the common difference (d) between consecutive terms by using the given information.
Given:
4th term + 7th term = 45
9th term = 117
Let's denote the 4th term as a and the common difference as d.
Since the 4th term + 7th term = 45, we can write this equation:
a + (a + 6d) = 45
Simplifying the equation, we get:
2a + 6d = 45 --------------- (Equation 1)
Since the 9th term = 117, we can write this equation:
a + 8d = 117 --------------- (Equation 2)
Now, let's solve these two equations to find the values of a and d.
From Equation 1, we can rewrite it as:
2a = 45 - 6d
a = (45 - 6d)/2
a = 22.5 - 3d
Substituting this value of a in Equation 2, we get:
22.5 - 3d + 8d = 117
5d = 117 - 22.5
5d = 94.5
d = 94.5 / 5
d = 18.9
Now, we have found the value of the common difference, which is d = 18.9.
To find the term when the sum is 600, we need to use the formula for the sum of an arithmetic series:
S = (n/2) * (2a + (n - 1) * d)
We know that the sum (S) is equal to 600.
Plugging in the values into the formula, we get:
600 = (n/2) * (2a + (n - 1) * 18.9)
Simplifying this equation will give us the value of n, which corresponds to the term when the sum is 600.
To find the term when the sum of it is 600, we need to identify the arithmetic sequence first.
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant. In this case, we are given that the sum of the 4th term and the 7th term is 45. This gives us the equation:
4th term + 7th term = 45
To find the common difference, we can subtract the 4th term from the 7th term since the difference between consecutive terms is constant. Let's call the common difference "d":
7th term - 4th term = d
Now that we have three equations, we can solve for the variables. By solving the first equation for the 4th term:
4th term = 45 - 7th term
Then plug in the second equation into the third equation:
(45 - 7th term) + 7th term = 117
Simplifying:
45 - 7th term + 7th term = 117
45 = 117
This equation is inconsistent, and that means there is no valid solution. Therefore, there is no term in the sequence that will have a sum of 600.