Sarvesh K Verma Solutions for Chapter: Sequence, Series & Progressions, Exercise 1: Introductory Exercise

If the $\mathrm{nth}$ term of an $\mathrm{AP}$ is $4\mathrm{n}-1,$ find the $30\mathrm{th}$ term and the sum of first $30$ terms.

Find the number of terms of the $\mathrm{AP} 98,91,84,\dots$ must be taken to give a sum of zero :

What is the greatest possible sum of the $\mathrm{AP} 17,14,11,\dots :$

What is the least possible sum of the $\mathrm{AP} -23,-19, -15,\dots :$

If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be the $\mathrm{pth}, \mathrm{qth}$ and $\mathrm{rth}$ terms of an $\mathrm{AP},$ then $\mathrm{p}(\mathrm{b}-\mathrm{c})+\mathrm{q}(\mathrm{c}-\mathrm{a})+\mathrm{r}(\mathrm{a}-\mathrm{b})$ equals to :

If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be respectively the sum of first $\mathrm{p}, \mathrm{q}, \mathrm{r}$ terms of an $\mathrm{AP},$ then $\frac{\mathrm{a}}{\mathrm{p}}(\mathrm{q}-\mathrm{r})+\frac{\mathrm{b}}{\mathrm{q}}(\mathrm{r}-\mathrm{p})+\frac{\mathrm{c}}{\mathrm{r}}(\mathrm{p}-\mathrm{q})$ equals

Divide $20$ into four parts which are in $\mathrm{AP}$ and such that the product of the first and fourth is to the product of the second and third in the ratio $2:3.$ Find the product of the first and fourth term of the $\mathrm{AP}:$

The sum of the first $\mathrm{p}$ terms of an $\mathrm{AP}$ is $\mathrm{q}$ and the sum of the first $\mathrm{q}$ terms is $\mathrm{p}.$ Find the sum of the first $(\mathrm{p}+\mathrm{q})$ terms :