Embibe Experts Solutions for Chapter: Sequences and Series, Exercise 3: Exercise-3

Let $a_1, a_2, a_3,\dots .$ be in harmonic progression with $a_1=5$ and $a_{20}=25$. The least positive integer $n$ for which $a_n<0$ is

Let $a_1,a_2,a_3,\dots$ be terms of an $\mathrm{AP}$. If $\frac{a_1+a_2+\dots +a_p}{a_1+a_2+\dots +a_q}=\frac{p^2}{q^2},p\ne q$, then $\frac{a_6}{a_{21}}$ equals

If $a_1,a_2,\dots ,a_n$ are in $\mathrm{HP}$, then the expression $a_1{a}_2+a_2{a}_3+\dots +a_{n-1}{a}_n$ is equal to

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals

A person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{th}$ minute. If $a_1=a_2=\dots =a_{10}=150$  and $a_{10}$, $a_{11},\dots$ are in an $A.P.$ with common difference $-2$, then the time taken by him to count all notes is

A man saves $\mathrm{Rs}.200$ in each of the first three months of his service. In each of the subsequent months, his savings increases by $\mathrm{Rs}.40$ more than the savings of immediately previous month. His total saving from the start of service will be $\mathrm{Rs}.11040$ after

The sum of first $20$ terms of the sequence $0.7,0.77,0.777,...$ is

The sum of first $9$ terms of the series $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots$ is