Amit M Agarwal Solutions for Chapter: Sequence and Series, Exercise 1: Work Book Exercise 3.1

If$N$ which is the set of natural numbers, is partitioned into subsets $S_1=\left\{1\right\}$, $S_2=\left\{2,3\right\},S_3=\left\{4,5,6\right\}...,$ then the sum of the members in $S_{50}$ is

If $\frac{3+5+7+\dots +n \mathrm{terms}}{5+8+11+\dots +10 \mathrm{terms}}=7$, then the value of $n$ is

The sum of the first ten terms of an $\mathrm{AP}$ is four times the sum of the first five terms, then the ratio of the first term to the common difference is

If $p, q$ and $r$ are in $\mathrm{AP}$, then $p^3+r^3-8q^3$ is equal to

Consider an $\mathrm{AP}$ with first term$a$ and common difference $d$. Let $S_k$ denotes the sum of first $k$ terms. If $\frac{S_{kx}}{S_x}$ is independent of $x,$ then

If $a_1, a_2, a_3, \dots$ are in $\mathrm{AP}$ such that $a{}_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225$, then $a_1+a_2+a_3+\dots +a_{23}+a_{24}$ is equal to

If the numbers $a, b, c, d, e$ are in $\mathrm{AP},$ then the value $a-4b+6c-4d+e$ is

Sum of $n$ terms of the series $\frac{1}{\sqrt{2}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{11}}+\dots$ is