What is the sum of the finite arithmetic series?
(–5) + 0 + 5 + 10 + ... + 65
1. 900
2. 455
3. 450
4. 445
To find the sum of the arithmetic series, we first need to find the number of terms in the series. The first term is -5 and the last term is 65, with a common difference of 5.
The formula for finding the nth term of an arithmetic series is:
an = a1 + (n-1)d
65 = -5 + (n-1)5
65 = -5 + 5n - 5
70 = 5n
n = 14
Now, we can find the sum of the series using the formula:
Sn = n/2 * (a1 + an)
Sn = 14/2 * (-5 + 65)
Sn = 7 * 60
Sn = 420
So, the sum of the finite arithmetic series is 420.
Therefore, the answer is not in the options provided.