Find the indicated nth partial sum of the arithmetic sequence.
2, 10, 18, 26, . . ., n = 15
a = 2
d = 8
n = 15
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
Wouldn't the answer be 114
To find the indicated nth partial sum of an arithmetic sequence, you need to use the formula for the nth term of an arithmetic sequence and the formula for the sum of an arithmetic series.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
where a1 is the first term, n is the term number, and d is the common difference between consecutive terms.
In this case, the first term (a1) is 2 and the common difference (d) is 8 (the difference between consecutive terms).
So, the nth term of this arithmetic sequence is:
an = 2 + (n - 1)8
To find the sum of n terms in an arithmetic series, you can use the formula:
Sn = (n/2)(a1 + an)
where Sn is the sum of the first n terms, n is the number of terms, a1 is the first term, and an is the nth term.
For the partial sum when n = 15, you can substitute the values into the formulas:
an = 2 + (15 - 1)8
an = 2 + 14 * 8
an = 2 + 112
an = 114
Sn = (15/2)(2 + 114)
Sn = (15/2)(116)
Sn = 15 * 58
Sn = 870
Therefore, the indicated 15th partial sum of the arithmetic sequence 2, 10, 18, 26, . . . is 870.