Question 11 and 12, Exercise 4.3
Solutions of Question 11 and 12 of Exercise 4.3 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.
Question 11
Find $S_{\boldsymbol{n}}$ for arithmetic series. $a_{1}=3$, $a_{n}=-38$, $n=8$.
Solution.
Given $a_{1}=3$, $a_{n}=-38$, $n=8$, then
\begin{align}
S_n&=\frac{n}{2}[a_1+a_n] \\
\implies S_{8}&=\frac{8}{2}[3-38]\\
&=4\times[-35] \\
&=-140.
\end{align}
Hence $S_{8}=-140$. 
Question 12
Find $S_n$ for each arithmetic series. $a_{1}=85$, $n=21$, $a_{n}=25$.
Solution.
Given $a_{1}=85$, $n=21$, $a_{n}=25$, then
\begin{align}
S_n&=\frac{n}{2}[a_1+a_n] \\
\implies S_{21}&=\frac{21}{2}[85+25]\\
&=1155.
\end{align}
Hence $S_{21}=1155$.
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