Question 3 and 4, Exercise 4.1

Solutions of Question 3 and 4 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.

The $n$th term of the sequence is given, find the first 4 terms; the 10th term, $a_{10}$ and the 15 th term: $a_{n}=\frac{n}{n+1}$

Solution. Given $$a_n = \frac{n}{n+1}.$$ Then $$\begin{align*} a_1 &= \frac{1}{1+1} = \frac{1}{2}\\ a_2 &= \frac{2}{2+1} = \frac{2}{3}\\ a_3 &= \frac{3}{3+1} = \frac{3}{4}\\ a_4 &= \frac{4}{4+1} = \frac{4}{5}\\ \end{align*}$$ Now $$\begin{align*} a_{10} &= \frac{10}{10+1} = \frac{10}{11}\\ a_{15} &= \frac{15}{15+1} = \frac{15}{16} \end{align*}$$ So, $a_1 = \frac{1}{2},\quad a_2 = \frac{2}{3},\quad a_3 = \frac{3}{4},\quad a_4 = \frac{4}{5},\quad a_{10} = \frac{10}{11},\quad a_{15} = \frac{15}{16}.$

The $n$th term of the sequence is given, find the first 4 terms; the 10th term, $a_{10}$ and the 15 th term: $a_{15}$.$a_{n}=n^{2}+1$

Solution.

Do yourself.

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