Determine the sum of the following arithmetic series.
^22E_ k=1(-5k+12)
To find the sum of the arithmetic series, we can use the formula:
S = n/2 * (a1 + an)
where:
S = sum of the series
n = number of terms
a1 = first term
an = last term
In this series, we have:
n = 22
a1 = -5(1) + 12 = 7
an = -5(22) + 12 = -98
Substitute these values into the formula:
S = 22/2 * (7 - 98)
S = 11 * (-91)
S = -1001
Therefore, the sum of the arithmetic series is -1001.