What is the sum of the finite arithmetic series ?
(-5) +0+5+10+...+65
To find the sum of a finite arithmetic series, we can use the formula:
S_n = n/2 * (a_1 + a_n)
where:
S_n = sum of the series
n = number of terms in the series
a_1 = first term in the series
a_n = last term in the series
In this case:
a_1 = -5
a_n = 65
n = (65 - (-5)) / 5 + 1 = 15
S_n = 15/2 * (-5 + 65)
S_n = 15/2 * 60
S_n = 450
Therefore, the sum of the series (-5) + 0 + 5 + 10 + ... + 65 is 450.