H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Arithmetic Progressions, Exercise 5: REVISION EXERCISE

Show that the sum of all odd integers between $1$ and $1000$ which are divisible  by $3$ is $166833$.

The houses of a row are numbers consecutively from $1$ to $49$. There is a value of $x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of $x$.

A sum of $₹700$ is to be used for giving $7$ cash prizes to students of a school for their academic performance. If each prize is $₹20$ less than its preceding prize, find the value of each of the prizes.

In an $\mathrm{A}.\mathrm{P}.,$ prove that ${\mathrm{a}}_{\mathrm{m}+\mathrm{n}}+{\mathrm{a}}_{\mathrm{m}-\mathrm{n}}=2{\mathrm{a}}_{\mathrm{m}} ,$ where ${\mathrm{a}}_{\mathrm{n}}$ denotes ${\mathrm{n}}^{\mathrm{th}}$ term of the $\mathrm{A}.\mathrm{P}.$

For what value of $\mathrm{n}$, the ${\mathrm{n}}^{\mathrm{th}}$ terms of the $\mathrm{A}.\mathrm{P}. 63, 65, 67, ..$ and $3, 10, 17, ...$ are equal?

In November $2009$, the number of visitors to a zoo increased daily by $20$. If a total of $12300$ people visited the zoo in that month, find the number of visitors on $1^{\mathrm{st}}$ November $2009$.

The $4^{\mathrm{th}}$ term of an $\mathrm{A}.\mathrm{P}.$ is equal to $3$ times the first term and the $7^{\mathrm{th}}$ term exceeds twice the $3^{\mathrm{rd}}$ term by $1$. Find the $\mathrm{A}.\mathrm{P}.$

Find the sum of all multiples of $9$ lying between $300$ and $700$.