R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: Exercise 5C

The sum of the first $n$ terms of an $\mathrm{AP}$ is $\left(3n^2+6n\right)$.  Find the $15\mathrm{th}$ term of this $\mathrm{AP}$.

The sum of the first $n$ terms of an $\mathrm{AP}$ is given by $S_n=\left(3n^2-n\right)$. Find the co-efficient of $\mathrm{n}$ of its ${\mathrm{n}}^{\mathrm{th}}$ term.

The sum of the first $n$ terms of an $\mathrm{AP}$ is given by $S_n=\left(3n^2-n\right)$. Find its first term.

The sum of the first $n$ terms of an $\mathrm{AP}$ is given by $S_n=\left(3n^2-n\right)$. Find its common difference.

If $m^{\mathrm{th}}$ term of an $\mathrm{AP}$ is $\frac{1}{n}$ and $n^{\mathrm{th}}$ term is $\frac{1}{m}$ then determine the sum of its first $mn$ terms, and find the sum if $\mathrm{mn}=49$.

If the sum of $n$ terms of the series $\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+\dots$ is $\frac{1}{2}\left(kn-1\right)$, then find the value of $k$.

The sum of first $n$ terms of two APs are in the ratio $(3n+8):(7n+15)$. Find the ratio of their ${12}^{th}$ terms.

If the ratio in simplest form is $\frac{p}{q}$, then $q=?$

A child puts one five-rupee coin of her savings in the piggy bank on the first day. She increases her saving by one five-rupee coin daily. If the piggy bank can hold $190$ coins of five rupees in all, find $k$, if $\mathrm{k}=\frac{\mathrm{total} \mathrm{money} \mathrm{saved} \mathrm{by} \mathrm{child}}{\mathrm{number} \mathrm{of} \mathrm{days} \mathrm{she} \mathrm{can} \mathrm{contribute}}$.