Question 13 and 14, Exercise 4.3

Solutions of Question 13 and 14 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 $S_s$ for arithmetic series. $a_{1}=34$, $n=9$, $a_{n}=2$.

Solution.

Given $a_{1}=34$, $n=9$, $a_{n}=2$., then $$\begin{align} S_n&=\frac{n}{2}[a_1+a_n] \\ \implies S_{9}&=\frac{9}{2}[34+2]\\ &=162. \end{align}$$ Hence $S_{9}=162$.

Find $S_n$ for arithmetic series. $a_{1}=5$, $d=\frac{1}{2}$, $n=13$.

Solution.

Given: $a_{1}=5$, $d=\frac{1}{2}$, $n=13$, then $$\begin{align} S_n&=\frac{n}{2}[2a_1+(n-1)d] \\ \implies S_{13}&=\frac{13}{2}\left[2(5)+(13-1)\times \frac{1}{2}\right]\\ &=\frac{13}{2}\left[10+6\right]\\ &=104. \end{align}$$ Hence $S_{13}=104$.

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