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.

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 $a_n = 2n - 1$.

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 $a_n = 3^n$.

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