Answer:
779
Step-by-step explanation:
Given Arithmetic series is: 150+143+136+…+(-102)+(-109)
Here,
First term (a) = 150
Common difference (d) = 143 - 150 = - 7
[tex]n^{th}\: term:\:a_n = -109[/tex]
The formula for [tex]n^{th}\: term[/tex] of an arithmetic series is given as:
[tex]a_n = a +(n-1)d[/tex]
Plugging the values of a, d and [tex]a_n[/tex] in the above formula, we will find the number of terms that exist from 150 to (-109)
[tex]-109 = 150+(n-1)(-7)[/tex]
[tex]\implies\: -109 -150=(n-1)(-7)[/tex]
[tex]\implies\: -259=(n-1)(-7)[/tex]
[tex]\implies\: \frac{-259}{-7}=(n-1)[/tex]
[tex]\implies\: 37=n-1[/tex]
[tex]\implies\: 37+1=n[/tex]
[tex]\implies\: n=38[/tex]
Thus, there are total 38 terms in the given Arithmetic series.
Now,
Sum of n terms of an arithmetic series is given by the formula: [tex]S_n=\frac{n}{2}(a +a_n)[/tex],
Plugging in the values, we find:
[tex]S_{38}=\frac{38}{2}[150 +(-109)][/tex]
[tex]\implies S_{38}=\frac{38}{2}[150 +(-109)][/tex]
[tex]\implies S_{38}=19[150 -109][/tex]
[tex]\implies S_{38}=19[41][/tex]
[tex]\implies S_{38}=779[/tex]
