Tamil Nadu Board Solutions for Chapter: Numbers And Sequences, Exercise 14: Exercise 2.4

Find the first four terms of the sequence, whose $n^{\mathrm{th}}$ term is given by $a_n=2n^2-6$.

If the $n^{\mathrm{th}}$ term of the sequence $2, 5, 10, 17, \dots \dots$ is of the form $a{n}^2+b$, then find the value of $a+b$.

If the $n^{\mathrm{th}}$ term of the sequence $0, \frac{1}{2}, \frac{2}{3}, \dots ..$. is $\frac{k}{n}$, then find $k$

Find the $n^{\mathrm{th}}$ term of the sequence $3, 8, 13, 18, \dots \dots$.

Find $a_6$ and $a_{13}$ of the sequences, whose $n^{\mathrm{th}}$ term is given by $a_n=\frac{5n}{n+2}$.

Find $a_4$ and $a_{11}$ of the sequences whose $n^{\mathrm{th}}$ term is given by $a_n=-\left(n^2-4\right)$.

Find $a_8$ and $a_{15}$ whose $n^{\mathrm{th}}$ term is $a_n=\left\{\begin{array}{l}\frac{n^2-1}{n+3}; n \mathrm{is} \mathrm{even}, n\in \mathrm{N}\\ \frac{n^2}{2n+1}; n \mathrm{is} odd, n\in \mathrm{N}\end{array}\right.$.

If $a_1=1, a_2=1$ and $a_n=2a_{n-1}+a_{n-2}n\ge 3, n\in \mathrm{N}$. Then, find the first six terms of the sequence.