Sum of First n Natural Numbers

Q.

Which term of the A.P. 121, 117, 113 … is its first negative term?

[Hint: Find n for a_n < 0]

Q.

If $\frac{3+5+7+....n}{5+8+11+....10}=7$, then the value of $n$ is

1. $35$

2. $36$

3. $37$

4. $40$

Q.

Find the sum of first n even natural numbers.

Q. Question 1 (i)
Find the sum of the following APs.
(i) 2, 7, 12, …., to 10 terms

Q.

Find the sum of first $n$ odd natural numbers.

Q. if the 5th term of an A.p is zero, then show that its 33rd term is 4 times its12th term

Q.

Fill in the blanks in the following table, given that a is the first term, d the common difference and a_n the n^th term of the A.P.

	a	d	n	an
I	7	3	8	…...
II	− 18	…..	10	0
III	…..	− 3	18	− 5
IV	− 18.9	2.5	…..	3.6
V	3.5	0	105	…..

Q.

Show that $a_1,a_2,\cdots ,a_n\cdots$ form an AP where $a_n$ is defined as below

$a_n=3+4n$ . Also find the sum of the first $15$ terms in each case.

Q.

What does $R$ equal in Math?

Q.

The sum of the arithmetic sequence 5, 10, 15, 20 is

1. 100

2. 25

3. 50

4. 75

Q. ​The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Q.

A staircase consists of 20 steps. The length and breadth of each step is 100 $m$ and $\frac{1}{2}m$ respectively. The height of the lowermost step is $\frac{1}{2}m$ and the height of the subsequent step increases by $\frac{1}{2}m$. Find the volume in $m^3$ of the concrete required to make the staircase.

1. 5250

2. 2520

3. 5225

4. 5520

Q. Find the sum of the first 4 terms of the sequence 4, 8, 12, 16, 20, ........

1. 30
2. 20
3. 40
4. 60

Q. Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.

Q. In which of the following situations, the sequence of numbers formed will form an A.P.?

(i) The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre.

(ii) The amount of air present in the cylinder when a vacuum pump removes each time $\frac{1}{4}$ of their remaining in the cylinder.

Q

Q. Find the sum of the first n even natural numbers. Hence find the sum of the first 20 even natural numbers.

Q. Find n if the given value of x is the nth term of the given A.P.

(i) 25, 50, 75, 100, ...; x = 1000

(ii) −1, −3, −5, −7, ...; x = −151

(iii) $5\frac{1}{2},11,16\frac{1}{2},22,...;x=550$

(iv) $1,\frac{21}{11},\frac{31}{11},\frac{41}{11},...,x=\frac{171}{11}$

Q.

Find the sum of all three-digit natural numbers, which are multiples of $11$.

Q.

The sum of three consecutive odd natural numbers is $111$. Find the numbers.

Q. Which of the following natural number lies between $\frac{3}{2}$ and $\frac{5}{2}$?

1. 3
2. 4
3. 1
4. 2

Q.

Find the sum of each arithmetic series

1). 38+35+32+......+2

Q. Question 2 (i)
Verify that each of the following is an AP and then write its next three terms.
$0,\frac{1}{4},\frac{1}{2},\frac{3}{4},\cdots$

Q.

Q. The sum of first 20 odd natural numbers is

(a) 100
(b) 210
(c) 400
(d) 420

Q.

In the $1908$Olympic Games, the Olympic marathon was lengthened from $40\mathrm{kilometers}$ to approximately $42\mathrm{kilometers}$. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? ($1\mathrm{mile}$ is approximately $1.6\mathrm{kilometers}$).

1. $1.00$

2. $1.25$

3. $1.50$

4. $1.75$

Q. How many terms of the A.P. (3, 5, 7, 9, ...) must be taken to get the sum as 120?

1. 9
2. 10
3. 11
4. 12

Q. Find the sum of all odd numbers between (i) 0 and 50 (ii) 100 and 200.

Q.

How many terms of an AP 27, 24, 21, ... are required to get the sum as 0?

1. 27

2. 19

3. 24

4. 17

Q.

The other name for literal numbers is

Q.

The first term of an A.P. is 12, the last term is -8, the common difference is -2. Find the sum of the A.P.

1. 20

2. 16

3. 22

4. 18