M L Aggarwal Solutions for Chapter: Arithmetic Progressions, Exercise 3: Execise 5.1

The number of bacteria in a certain item after each second, when they double in every second. Check whether the list of numbers involved in this situation make an arithmetic progression or not and why ?

Find the sum given below:

$\left(-5\right)+\left(-8\right)+\left(-11\right)+ ... +\left(-230\right)$

Find the sum of all three digit natural numbers which are multiples of $9$.

Find the sum of all two digit numbers which when divided by $7$ yield $1$ as the remainder.

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: $₹200$ for the first day, $₹ 250$for the second day, $₹300$ for the third day, etc., the penalty for each succeeding day being $₹50$ more than for the preceding day. If $₹k$ is the money the contractor has to pay as penalty, and he has delayed the work for $30$ days, then find $k$.

Kanika was given her pocket money on $1\mathrm{st} \mathrm{Jan}, 2019$. She puts $₹1$ on day $1, ₹2$ on day, $2, ₹3$ on day $3$, and continued doing so till the end of the month, from this money into her piggy bank. She also spent $₹204$ of her pocket money, and was found that at the end of the month she still had $₹100$ with her. If money $₹x$ was her pocket money for the month, find $x$.

Yasmeen saves $₹32$ during the first month, $₹36$ in the second month and $₹40$ in the third month. If she continues to save in this manner, in how many months will she save $₹2000$?

A thief, after committing a theft runs at a uniform speed of$50 \mathrm{m}/\mathrm{minute}$. After $2 \mathrm{minutes}$, a policeman runs to catch him. He runs $60 \mathrm{m}$ in first minute and increases his speed by $5 \mathrm{m}/\mathrm{minute}$ every succeeding minute. After how many minutes, the policeman will catch the thief?