# 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 $a_n=\sqrt{2n}$.

## 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 $a_n=1.1n+0.1$.

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