A P Prabhakaran Solutions for Chapter: Sequence and Series, Exercise 3: OBJECTIVE TYPE QUESTIONS

The first term of an arithmetic progression having all integral terms is the square of the common difference. The sum of the first $4$ terms of the arithmetic progression is $54$. Find the common difference.

Ganga increases the speed of her vehicle by $4 \mathrm{km}/\mathrm{hr}$ every $2$ minutes. If the speed of her vehicle becomes $44 \mathrm{km}/\mathrm{hr}$ at $2.\mathrm{p}.\mathrm{m}.$ then at what time the speed will becomes $128 \mathrm{km}/\mathrm{hr}$?

If the sides of a right angled triangle have integral lengths which form an $\mathrm{A}.\mathrm{P}.,$ then one of the sides (length) could be

The sum of the first $7$ terms in a series of $10$ terms in an arithmetic progression is $28$ while the sum of the last seven terms is $49$. What is the sum of all the $10$ terms? 

At Mumbai bus depot there are $1024$ buses. Every hour, half the buses depart for different destinations. After how many hours, does the depot have only one bus?

$100$ arithmetic means are inserted between $x$ and $y$. The common difference $d$ is

If $l, m, n, p, q, r, s$ and $t$ are in arithmetic progression, then the ratio of $(r -t)$ and$(p -n)$ is 

The municipal corporation authorities decided to plant trees on either side of a highway. The sum of all the numbers allotted to the trees was $1260$. Find the total number of trees on the highway if the first tree is numbered as $0, 2^{\mathrm{nd}}$ as $2$ and $3^{\mathrm{rd}}$ as $4$ and so on.