If the sum of the first 15 terms of an arthimetic sequence is 240. what is the 8th term
To find the 8th term of an arithmetic sequence, we need to know the formula for the sum of the first n terms of an arithmetic sequence. The formula for the sum of an arithmetic sequence is:
Sn = (n/2)(2a + (n-1)d)
where Sn represents the sum of the first n terms, a represents the first term, and d represents the common difference between each term.
In this case, we are given that the sum of the first 15 terms (Sn) is 240. We want to find the 8th term, so n = 8.
240 = (8/2)(2a + (8-1)d)
240 = 4(2a + 7d)
Divide both sides of the equation by 4:
60 = 2a + 7d
Now, we have an equation with two variables (a and d). We need one more equation to solve for the values of a and d.
Unfortunately, we don't have the information necessary to find the values of a and d in this problem. Therefore, we cannot determine the 8th term of the arithmetic sequence given only the sum of the first 15 terms.
To find the 8th term of an arithmetic sequence, we first need to determine the common difference. This can be done by using the formula for the sum of an arithmetic sequence.
The formula for sum of an arithmetic sequence is given by:
Sn = n/2 * (2a + (n-1)d)
where Sn is the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.
In this case, we are given that the sum of the first 15 terms is 240. Therefore, we can set up the equation:
240 = 15/2 * (2a + (15-1)d)
Simplifying, we get:
240 = 7.5(2a + 14d)
16 = 2a + 14d
Now, we can use the fact that the 8th term can be expressed using the first term (a) and the common difference (d) as:
8th term = a + 7d
Since we have an equation with two unknowns (a and d), we need another equation to solve for them. We can use the fact that the 16th term can also be expressed in terms of a and d:
16th term = a + 15d
Now, we have a system of two equations with two variables:
16 = 2a + 14d
8th term = a + 7d
By solving this system of equations, we can find the values of a and d. Once we have those values, we can substitute them back into the equation for the 8th term to find the answer.