What is the sum of the finite arithmetic series?

(–5) + 0 + 5 + 10 + ... + 65

1. 900

2. 455

3. 450

4. 445

1 answer

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.