Question
Find the sums given below : – 5 + ( – 8) + ( – 11) + … + ( – 230)
✓
Answer
$
-5+(-8)+(-11)+\ldots+(-230)
$
Here, $a=-5, d=-8-(-5)=-8+5=3$
$
\begin{aligned}
& I=-230 \\
& \therefore I=a+(n-1) d \\
& \Rightarrow-230=-5+(n-1)(-3) \\
& -230+5=-3(n-1) \\
& \Rightarrow-225=-3(n-1) \\
& \frac{-225}{-3}=n-1 \\
& \Rightarrow n-1=75 \\
& \Rightarrow n=75+1=76 \\
& \therefore S_n=\frac{n}{2}[a+l] \\
& =\frac{76}{2}[-5+(-230)] \\
& =38[-5-230] \\
& =38 \times(-235) \\
& =-8930 .
\end{aligned}
$
-5+(-8)+(-11)+\ldots+(-230)
$
Here, $a=-5, d=-8-(-5)=-8+5=3$
$
\begin{aligned}
& I=-230 \\
& \therefore I=a+(n-1) d \\
& \Rightarrow-230=-5+(n-1)(-3) \\
& -230+5=-3(n-1) \\
& \Rightarrow-225=-3(n-1) \\
& \frac{-225}{-3}=n-1 \\
& \Rightarrow n-1=75 \\
& \Rightarrow n=75+1=76 \\
& \therefore S_n=\frac{n}{2}[a+l] \\
& =\frac{76}{2}[-5+(-230)] \\
& =38[-5-230] \\
& =38 \times(-235) \\
& =-8930 .
\end{aligned}
$
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