Embibe Experts Solutions for Chapter: Arithmetic Progressions, Exercise 1: Rajasthan Board-2018

If second and third terms of an Arithmetic Progression are $3$ and $5$ respectively, then find the sum of first $20$ terms of it.

If fare of a car for first kilometer is $₹20$ and for after $1$ kilometer is $₹11$, then find the total fare for $15$ kilometers.

The distance between $A$ and $B$ is $125 \mathrm{km}$ and there are Eight $\left(8\right)$ traffic signals in between $A$ and $B$. If a car by $50 \mathrm{km}/\mathrm{h}$ speed reaches point $B$ crossing all green signals in $2$ hours and $30$ minutes but on other days due to heavy traffic it happens to stop as follows. First Traffic Signal$-1$ minute, Second Traffic Signal$-2$ minutes and up to Eight$\left(8\mathrm{th}\right)$ signal$-8$ minutes. Calculate the total time taken by that car if it follows the total traffic signals.

Find the sum of all the natural numbers divisible by $5$ between $2$ and $101$.

A car passes through a first signal in $3$ minutes, second in $6$ minutes, third in $9$ minutes. In how much time it passes through ${13}^{\mathrm{th}}$ signal?

If second and third terms of an A.P. are $24$ and $28$ respectively, then find the sum of first $61$ terms.