Embibe Experts Solutions for Chapter: Sequence and Series, Exercise 1: JKCET 2017

If the three consecutive terms of an arithmetic sequence are $x,(2 x+1)$ and $11,$ then the value of $\text{'}x\text{'}$ is

In an arithmetic sequence the ${21}^{\text{st }}$ term is $170$ and the $5^{\text{th }}$ term is $122.$ What is the third term in the sequence?

If $60$ times the ${60}^{\text{th }}$ term of an $\mathrm{AP}$ with non zero common difference is equal to $40$ times the ${40}^{\text{th }}$ term, then the ${100}^{\text{th }}$ term of this $\mathrm{AP}$ is

What is the sum value of the geometric series $6+3+3/2+3/4+\dots \infty ?$

How many digits will be there after the decimal point ${12}^{\mathrm{th}}$ term of the sequence: $32, 16, 8, 4, \dots \dots ?$

$A$ set $P$ is taken such that $P=\left\{2/3^p\mid p\right.$ is a natural number $\}.$ What will be the sum of elements of set $P ?$

It is given that $P=$Sum of all integral powers of $\left(\frac{4}{5}\right)$ from $1$ to $n$. Also, $Q=1-P$. The smallest natural number for which $Q>P$ is

The sum value of the series $\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\dots \dots .\infty$ is