====== Question 21 and 22, Exercise 4.1 ======
Solutions of Question 21 and 22 of Exercise 4.1 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 21=====
Predict the general term or nth term, $a_{n}$, of the sequence. $\sqrt{2}, \sqrt{4}, \sqrt{6}, \sqrt{8}, \sqrt{10}, \ldots$

** Solution. **

The given sequence is $$\sqrt{2}, \sqrt{4}, \sqrt{6}, \sqrt{8}, \sqrt{10}, \ldots$$ 	
The terms can be rewritten as:
\begin{align*}
&a_1=\sqrt{2 \cdot 1}, \\
&a_2=\sqrt{4}=\sqrt{2 \cdot 2} \\
&a_3=\sqrt{6}=\sqrt{2 \cdot 3}\\
&a_4=\sqrt{8}=\sqrt{2 \cdot 4}\\
&a_5=\sqrt{10}=\sqrt{2 \cdot 5}
\end{align*}
Thus, we can predict $a_n=\sqrt{2n}$. GOOD





=====Question 22=====
Predict the general term or nth term, $a_{n}$, of the sequence. $1.2,2.3,3.4,4.5, \ldots$

** Solution. **
The given sequence is in arithmetic in which
$a_1=1.2$, $d=2.3-1.2=1.1$, thus
\begin{align*}
a_n &= a + (n - 1) d\\
&=1.2+(n-1)(1.1)\\
&=1.2+1.1n-1.1\\
&=1.1n+0.1
\end{align*}
Thus the general term is $a_n=1.1n+0.1$. GOOD




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