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

If $n$ arithmetic means are inserted between $1$ and $31$ such that the ratio of the first mean and $n$th mean is $3 : 29,$ then the value of $n$ is

If four numbers in $\mathrm{A}.\mathrm{P}.$are such that their sum is $50$ and the greatest number is $4$ times the least, then the numbers are

If $a_1 ,a_2, a_3, \dots , a_n$are in $\mathrm{A}.\mathrm{P}$. with common difference $d$, then the sum of the series $\sin d \left[\sec a_1\sec a_2+\sec a_2\sec a_3+\dots .+\sec a_{n-1}\sec a_n]\right.$, is

In$\mathrm{A}.\mathrm{M}.\text{'}\mathrm{s}$ are introduced between $3$ and $17$ such that the ratio of the last mean to the first mean is $3 : 1,$ then the value of $n$ is

Sum of all two digit numbers which when divided by $4$ yield unity as remainder is

$x, y \mathrm{and} z$ are positive integers, then the value of expression $\left(x+y\right)\left(y+z\right)\left(z+x\right)$ is

If $a_1, a_2, a_3, \dots , a_n\text{ are in A.P. }$with common difference $d$, then the sum of the series $\sin d$$\left[cosec{a}_{1}cosec{a}_2+cosec{a}_{2}cosec{a}_3+\dots .+cosec{a}_{n-1}cosec{a}_n\right]\text{ is }$

If $1^2+2^2+3^2\dots .+{\mathrm{x}}^2=\frac{\mathrm{x}(\mathrm{x}+1)(2\mathrm{x}+1)}{6}$, then $1^2+3^2+5^2\dots +{19}^2$ is equal to: