Question 7 and 8, Exercise 4.3
Solutions of Question 7 and 8 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 7
Find the sum of series. $9+11+13+15+\cdots$ for $n=12$
Solution.
Given series is arithmetic series with $a_1=9$, $d=11-9=2$, $n=12$.
Let $S_n$ represents sum of the arithmetic series. Then
\begin{align}
S_n&=\frac{n}{2}[2a_1+(n-1)d] \\
\implies S_{12}&=\frac{12}{2}[2(9)+(12-1)(2)]\\
&=6\times [18+22]\\
&=240.
\end{align}
Hence $S_{12}=240$. 
Question 8
Find the sum of the even numbers from $2$ to $100$.
Solution.
Sum of the even numbers from $2$ to $100$ is
$$2+4+6+...+100 (50 \text{ terms}).$$
This is arithmetic series with: $a_{1}=2$, $n=50$, $d=4-2=2$.
Let $S_n$ represents sum of the arithmetic series. Then
\begin{align}
S_n&=\frac{n}{2}[2a_1+(n-1)d] \\
\implies S_{50}&=\frac{50}{2}[2(2)+(50-1)(2)]\\
&=25\times [4+98]\\
&=2550.
\end{align}
Hence the sum of the even numbers from $2$ to $100$ is $2550$.
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