Jitender Gupta and Divya Malik Solutions for Exercise 5: CHAPTER EXERCISE

If $\mathrm{a}, \mathrm{b} \mathrm{and} \mathrm{c}$ are the $1\mathrm{st}, 3\mathrm{rd} \mathrm{and} \mathrm{nth} \mathrm{terms}$ respectively of an $\mathrm{AP}$, then prove that the sum to $\mathrm{n}$ terms is $\frac{c+a}{2}+\frac{c^2-a^2}{b-a}.$

Sum of the first $\mathrm{n}$ terms of an $\mathrm{A}.\mathrm{P}$ is $5{\mathrm{n}}^2-3\mathrm{n}$. Find the $\mathrm{A}.\mathrm{P}$ and also find its ${16}^{\mathrm{th}}$ term.

Find the sum of all two-digit odd positive numbers.

Each year, a tree grows $5 \mathrm{cm}$ less than it did the preceding year. If it grew by $1 \mathrm{m}$ in the first year, then in how many years will it have ceased growing? 

Komal decides to solve two questions of Mathematics first day and doubles the number every day. In how many days will she be able to solve the total questions $2046$ in the book ?

Rohit borrows $₹10000$ from his friend, Mohit. Mohit asks him to return the money just by repaying $₹10$ at first day and double the amount in the subsequent days than the each previous day continuously for only ten days. Rohit thanks Mohit for his help. Now, determine whether Mohit was in loss or profit.

$150$ workers were engaged to finish a job in a certain number of days, $4$ workers dropped out on second day, $4$ more workers dropped out on third day and so on. It took $8$ more days to finish the work. Find the number of days in which the work was completed.

A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with the instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs  $25$ paise to mail one letter, determine the amount spent on postage when the $8$ th set of letters is mailed.