Embibe Experts Solutions for Chapter: Sequence and Series, Exercise 1: KEAM 2019

The value of $\sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-\dots \infty }}}}$ is

In an A.P., the first term is $3$ and the last term is $17$. The sum of all the terms in the sequence is $70$. Then the number of terms in the arithmetic sequence is

If $\mathrm{p},\mathrm{q}$ and $23$ is an increasing arithmetic sequence and $\mathrm{p}$ and $\mathrm{q}$ are prime numbers, then $\mathrm{p}+\mathrm{q}=$

If an $\mathrm{AP}, a_7=9$ if $a_1{a}_2{a}_7$ is least, the common difference is

The $5^{\mathrm{th}}$ and $7^{\mathrm{th}}$ term of a G.P. are $12$ and $48$ respectively. Then the $9^{\text{th }}$ term is 

Let $\left\{a_n\right\}$ be a $GP$such that $\frac{a_4}{a_6}=\frac{1}{9}$ and $a_2+a_5=1$ then first term is

If $m_1,m_2,m_3\dots m_{20}$ are $\mathrm{AMs}$ between $13$ and $67,$ then maximum value of $m_1{m}_2{m}_3\dots m_{20}$ is

Consider the set of all positive rational numbers that are less than $1$ and that have denominätors as $30$ in their lowest terms. Their sum is equal to