Formula for Sum of n Terms of an AP

Q.

Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21.

Q.

How many terms of the AP: 9, 17, 25, ... must be added to get a sum of 636?___

Q.

The sum of $4\mathrm{th}$and $8\mathrm{th}$ terms of an A.P. is $24$ and the sum of the $6\mathrm{th}$ and $10\mathrm{th}$ terms is $44$. Find the first three terms of the A.P.

Q.

On dividing a positive integer $n$ by $9$ we get $7$ as remainder. What will be the remainder if $(3n-1)$ is divided by $9$?

Q. If n = 2³ ✕ 3⁴ ✕ 5⁴ ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is

(a) 2
(b) 3
(c) 4
(d) 7

Q.

The number lies between 100000 and 110000 which is exactly divisible by 8, 15 and 21 is

Q.

What is the largest four digit number which is exactly divisible by 88 what are the steps to find it

Q.

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by 7. The common difference is 2.

1. False

2. True

Q.

What is the relation between AP, GP, and HP?

Q.

The organizers of an essay competition decide that a winner in the competition gets a prize of $₹100$ and a participant who does not win gets a prize of $₹25$‘. The total prize money distributed is ’$₹3000$‘. Find the number of winners, if the total number of participants is ’$63$.

Q.

A train leaves Delhi at 6:00 am and reaches Haridwar at 10:00 am. Another train leaves Haridwar at 8:00 am and reaches Delhi at 11:30 am. At what time the trains meet?

Q.

If $A=\{1,2,3\}$, $B=\{3,4\}$ and $C=\{4,5,6\}$, then $A\cup (B\cap C)$ is equal to

1. $\{1,2,\}$

2. $\varnothing$

3. $\{4,5\}$

4. $\{1,2,3,4\}$

Q.

How many terms of the AP 3, 7, 11, 15, ... willl make the sum 406 ?
(a) 10 (b) 12 (c) 14 (d) 20

Q.

Find the sum of the first 15 multiples of 8.

Q.

A child puts one five rupee coin from her saving in the piggy bank on the first day. She increases her saving by one five - rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the number of days she can contribute to putting the five rupees of into it and find the total money she saved.

Q.

What is the sum of all odd numbers between $0\text{and}100$?

Q.

In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is $25$. Then, the sum of $4th,6thand8th$ terms is equal to:

1. $35$

2. $30$

3. $26$

4. $32$

Q. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Q. The sum of all integers between 200 and 300 which are divisible by both 5 and 3 is

1. 854
2. 1485
3. 1548
4. 1500

Q. Find the fourth term from the end in an A.P. –11, –8, –5, ...., 49.

Q. Question 16
A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

Q.

The students of a school decided to beautify the school on the annual day by fixing colourful on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 meter. The flags are stored at the position of the middle most flag. Ruchi was given the responsiblity of palcing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Q.

Find the sum : 34 + 32 + 30 + .... + 10

1. 300

2. 286

3. 310

4. 240

Q.

If $m^{th}$ term of an AP is $\frac{1}{n}$ and $n^{th}$ term is $\frac{1}{m}$ then find the sum of its first $mn$ terms.

Q.

Find the number of three digit natural numbers which are divisible by 11

Q. What is the remainder when 7^700 divided by 100 ?

Q.

How many terms of the AP: 21, 18, 15, ... must be added to get the sum 0?

Q. Question 3 (i)
In an AP:
(i) Given a = 5, d = 3, $a_n=50$, find n and $S_n$.

Q.

If the sum of the first n terms of an AP is 4n-n2 what is the first term that is S1 ? What is the sum of first two terms? What is the second term similarly find the third and 10th and nth terms

Q.

The ${17}^{th}$ term of $AP$ is $5$ more than twice it's $8^{th}$ term. If the ${11}^{th}$ term of the AP is $43$, find its $n^{th}$ term