Question

Find the sum of an arithmetic series written as Σ 20 k = 1 (− 3 k +2)

(20 on top and k=1 on the bottom of Σ )

Answer 1

The formula for the sum of an arithmetic series is:

S = n/2 [2a + (n-1)d]

where:

S = the sum of the arithmetic series
n = the number of terms in the series
a = the first term in the series
d = the common difference between the terms in the series

In this case, we have:

a = -3k + 2
d = -3
n = 20

Substituting these values into the formula, we get:

S = 20/2 [2(-3(1)) + (20-1)(-3)]
S = 10 [-6 -57]
S = 10 [-63]
S = -630

Therefore, the sum of the arithmetic series is -630.