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:

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

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

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

$S_19 = 19/2xx70$

$S_19 = 665$

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