Embibe Experts Solutions for Chapter: Arithmetic Progressions, Exercise 1: Exercise

Check whether the given list of numbers forms $\mathrm{AP}$ or not? If they form an $\mathrm{AP}$, find the common difference $d$ and write the next three terms.

$a, a^2, a^3, a^4,\dots ....$

The sum of the $2^{\text{nd }}$ term and the $7^{\text{th }}$ term of an A.P. is $30 .$ If its ${15}^{\text{th }}$term is $1$ less than twice of its $8^{\text{th }}$ term, find the A.P.

Write first four terms of the $\mathrm{AP},$ when the first term $a$ and the common difference $d$ are given as $a=-1,d=\frac{1}{2}$.

Find the respective terms for the given terms of an $\mathrm{AP}.$.

$a_2=13, a_4=3$ find $a_1, a_3$

If four numbers are in AP such that their sum is $50$ and the greatest number is $4$ times the least, then find the numbers.

Split $210$ into three parts such that these are in A.P and the product of the two greatest parts is $5110$. Find the three parts.

Does the following form an A.P? Justify your answer.

$1,1,2,2,3,3,.........$

The ${\left(n – 1\right)}^{\mathrm{th}}$ term of an A.P. is given by $7,12,17, 22,\dots$ is