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.

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 $S_{8}=-140$.

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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