What is the sum of the finite arithmetic series?

Question

(–5) + 0 + 5 + 10 + ... + 65

Answer 1

The first term of the arithmetic series is -5, the common difference is 5, and the last term is 65.

To find the number of terms in the series, we can use the formula for the nth term of an arithmetic series:

an = a1 + (n-1)d

65 = -5 + (n-1)5

70 = 5(n-1)

n = 15

Now, we can use the formula for the sum of an arithmetic series:

Sn = n/2 * (a1 + an)

Sn = 15/2 * (-5 + 65)

Sn = 15/2 * 60

Sn = 450

Therefore, the sum of the finite arithmetic series is 450.