====== Question 19 and 20, Exercise 4.1 ======
Solutions of Question 19 and 20 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 19=====
Predict the general term or nth term, $a_{n}$, of the sequence. $1,3,5,7,9, \ldots$

** Solution. **
Given $$1, 3, 5, 7, 9, \ldots$$ 
This is arithmetic sequence with $a_1=1$, $d=3-1=2$. Thus
$$a_n = a_1 + (n - 1) d$$	
\begin{align*}
\implies a_n &= 1 + (n - 1) \cdot 2\\
 &= 1 + 2n - 2\\
&= 2n - 1 \end{align*}
So, the general term is $a_n = 2n - 1$. GOOD

=====Question 20=====
Predict the general term or nth term, $a_{n}$, of the sequence.$3,9,27,81,243, \ldots$

** Solution. **

\begin{align}
& a_1=3 \\
& a_2 = 9 = 3^2 \\
& a_3 = 27 = 3^3 \\
& a_4 = 81 = 3^4
\end{align}
So, we can predict the general term is $a_n = 3^n$. GOOD



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