# 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 $a_n = 2n - 1$.

## 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 $a_n = 3^n$.

### Go to