Find the indicated nth partial sum of the arithmetic sequence.
2, 10, 18, 26, . . ., n = 15
looks like a=2, d=8, n=15
Sum(15) = (15/2)(4 + 14(8))
= ...
To find the nth partial sum of an arithmetic sequence, we can use the formula:
Sn = (n/2)(a1 + an)
where Sn represents the sum of the first n terms, n is the number of terms, a1 is the first term, and an is the nth term.
In this case, we are given the arithmetic sequence: 2, 10, 18, 26, ...
We need to find the sum of the first 15 terms, so n = 15.
First, let's find the values of a1 and an.
The first term, a1, is 2.
To find the nth term, an, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where d is the common difference of the sequence. In this case, the common difference is 10 - 2 = 8.
So, an = 2 + (15 - 1)8 = 2 + 14*8 = 2 + 112 = 114.
Now we can substitute these values into the formula for the nth partial sum:
Sn = (n/2)(a1 + an)
= (15/2)(2 + 114)
= (15/2)(116)
= 15 * 58
= 870.
Therefore, the 15th partial sum of the arithmetic sequence 2, 10, 18, 26, ... is 870.
To find the nth partial sum of an arithmetic sequence, we can use the formula:
Sn = [n/2] * (2a + (n-1)d)
where Sn is the nth partial sum, n is the number of terms, a is the first term, and d is the common difference.
Given the arithmetic sequence:
2, 10, 18, 26, ...
n = 15
a = 2 (first term)
d = 8 (common difference, obtained by subtracting the second term from the first term)
Substituting the values into the formula:
Sn = [15/2] * (2(2) + (15-1)(8))
= [15/2] * (4 + 14(8))
= [15/2] * (4 + 112)
= [15/2] * (116)
= 15/2 * 116
= 870
Therefore, the 15th partial sum of the given arithmetic sequence is 870.