Question 3 and 4, Exercise 4.3
Solutions of Question 3 and 4 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 3
Find the sum of each series. $a_{1}=5$, $a_{n}=100$, $n=200$
Statement is logically incorrect.
Find the sum of arithmetic series with: $a_{1}=5$, $a_{n}=100$, $n=200$.
Solution.
Given $a_{1}=5$, $a_{n}=100$, $n=200$.
Let $S_n$ represents sum of arithmetic series. Then
\begin{align}
S_n&=\frac{n}{2}[a_1+a_n] \\
\implies S_{200}&=\frac{200}{2}[5+100]\\
&=10500.
\end{align}
Hence $S_{200}=10500$. 
Question 4
Find the sum of series. $a_{1}=4$, $n=15$, $d=3$.
Statement is logically incorrect.
Find the sum of arithmetic series with: $a_{1}=4$, $n=15$, $d=3$.
Solution.
Given: $a_{1}=4$, $n=15$, $d=3$.
Let $S_n$ represents sum of arithmetic series. Then
\begin{align}
S_n&=\frac{n}{2}[2a_1+(n-1)d] \\
\implies S_{15}&=\frac{15}{2}[2(4)+(15-1)(3)]\\
&=\frac{15}{2}[50]\\
&=375.
\end{align}
Hence $S_{15}=375$.
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