Find the next three terms of the sequence $5, 1,-3,\dots$.

Find the next three terms of the sequence $\frac{1}{4}, \frac{2}{9}, \frac{3}{16},\dots \dots \dots$.

Find the first four terms of the sequence whose $n^{\mathrm{th}}$ term is given by $a_n=n^3-2$.

Find the first four terms of the sequence whose $n^{\mathrm{th}}$ term is given by $a_n=(-1{)}^{n+1}n(n+1)$.

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 $a_n=\frac{5n}{n+2}$.