Embibe Experts Solutions for Chapter: Sequences and Series, Exercise 1: Level 1

The maximum sum of the series $20+19\frac{1}{3}+18\frac{2}{3}+18+\dots$ is

Three positive numbers form an increasing $\mathrm{G}.\mathrm{P}.$ If the middle term in the $\mathrm{G}.\mathrm{P}.$ is doubled the three numbers are in an $\mathrm{A}.\mathrm{P}.$ Then the common ratio of the $\mathrm{G}.\mathrm{P}.$ is

The sum of series, $6+66+666+........$ upto $n$ term is -

The value of $x$ in $(-\pi ,\pi )$ which satisfies the equation $8^{1+\left|\cos x\right|+\left|{\cos }^{2}x\right|+|{\cos }^{3}x\mid +\dots \dots \infty }=4^3$ is -

Three numbers whose product is $512$ are in $G.P.$ If $8$ is added to the first and $6$ to the second, the number will be in $A.P.$ The numbers are -

If $a, b, c$ form a $G.P.$ with common ratio $r$ such that $0<r<1$, and if $a, \frac{3b}{2}, -4c$ form an $A.P.$, then $r$ is equal to -

The sum of $n$ terms of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+..$ is

Let $a, b, c, d$ and $e$ be distinct positive numbers. If $a, b, c$ and $\frac{1}{c}$, $\frac{1}{d}$, $\frac{1}{e}$ both are in $\mathrm{AP}$ and $b, c, d$ are in $\mathrm{GP}$, then