Q. $a_n=n\frac{n^2+5}{4}$

Q. $a_n=\frac{n^2}{2^n};a_7$

Q. $a_n=\frac{2n-3}{6}$

Q.

To find first five terms of the given series $a_1=3,a_n={3a}_{n-1}+2$ for all $n>1$ and hence find the corresponding series.

Q. $a_n=(-1{)}^{n-1}{n}^3;a_9$

Q. $a_n=\frac{n(n-2)}{n+3};a_{20}$

Q. The Fibonacci sequence is defined by $1=a_1=a_2=2,a_n=a_{n-1}+a_{n-2},n>2.$ Find $\frac{a_{n+1}}{a_n},$ for $n=1,2,3,4,5$

Q. $a_1=a_2=2,a_n=a_{n-1}-1,n>2$

Q. $a_n=4n-3;a_{17},a_{24}$

Q. $a_1=-1,a_n=\frac{a_{n-1}}{n},n\ge 2$

Q. $a_n={(-1)}^{n-1}{5}^{n+1}$

Q. $a_n=n(n+2)$

Q. $a_n=2^n$

Q. $a_n=\frac{n}{n+1}$

Q. If the sum of a certain number of terms of the A.P. $25,22,19,...$ is $116$. Find the last term.

Q. Find the sum of all natural numbers lying between $100$ and $1000$, which are multiples of $5$.

Q. How many terms of the $A.P$. $-6,-\frac{11}{2},-5,...$ are needed to give the sum $-25$?

Q. In an A.P., if $p^{th}$ term is $\frac{1}{q}$ and $q^{th}$ term is $\frac{1}{p}$, prove that the sum of first $pq$ terms is $\frac{1}{2}(pq+1)$, where $p\ne q$.

Q. Find the sum of odd integers from $1$ to $2001$.

Q. In an $A.P$., the first term is $2$ and the sum of the first five terms is one-fourth of the next five terms. Show that ${20}^{th}$ term is $-112$.