How do you find the sum of the first 19 terms of the series #-10+(-5)+0+5+10+...#?

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Answer 1 · 2016-12-03T18:21:03

#S_19 = 665#

Identify what you know about this series:

#1. # It is arithmetic.

#2. " "a = -10" "# (the first term)
#" "d = +5" "# (the common difference)
#" "n = 19" "# (there are 19 terms)

#3" " # The required formula for the sum of an arithmetic series is:

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

So now it just remains to substitute into the formula:

#S_19 = 19/2[2(-10) + (19-1)xx(5)]#

#S_19 = 19/2[-20 + (18)xx(5)]#

#S_19 = 19/2[-20 + 90]#

#S_19 = 19/2xx70#

#S_19 = 665#