What is the sum of the series ?

Question

What is the sum of the series ? 6 (-3k+5)

k=3

_______

 

(there is a big E looking symbol suppose to be under the 6)

Answer 1

That big E looking symbol is ∑. It is the Greek letter sigma. It represents the sum of a series.

 

This series starts with k = 3 and ends with k = 6.

 

1st term = -3(3) + 5 = -9 + 5 = -4

2nd term = -3(4) + 5 = -12 + 5 = -7

3rd term = -3(5) + 5 = -15 + 5 = -10

 

-4 + (-7) + ) + (-10)

-21

 

The sum of the series is -21.

 

Using the formula for the sum of an arithmetic series: S_n = n[2a₁ + (n - 1)d ] /2, where S = the sum, n = number of terms, d = common difference, a₁ = -4_.

 

S₃ = 3[2(-4) + (3 - 1)(-3)] / 2

S₃ = 3[-8 + 2(-3)] / 2

S₃ = 3[-14]/2

S₃ = -21