Sum of Consecutive Numbers

Q. Find out the sum of first 20 natural numbers:

1. 210
2. 230
3. 200
4. 420

Q. The sum of first 6 natural numbers is .

1. 21
2. 20
3. 42

Q. Find the sum of all the natural numbers between 1 to 100 which are divisible by 6.

1. 814
2. 816
3. 812
4. 820

Q. Find the sum of integers from 1 to 100 which are divisible by 2 or 3.

1. 3412
2. 3417
3. 3422
4. 3401

Q. Find the sum of integers which are divisible by 5 from 50 to 85?

1. 540
2. 600
3. 550
4. 560

Q. The sum of the first n consecutive natural numbers is a number.

1. negative
2. square
3. triangular
4. cubic

Q. Find the sum of all the natural numbers which are divisible by 4 from 20 to 100.

1. 1200
2. 1300
3. 1240
4. 1260

Q.

Express $\frac{2}{-9}$ as a rational number with a numerator $-8$

Q. The sum of first 50 natural numbers which are divisible by 2 is .

1. 650
2. 425
3. 325

Q. Which of the following options demonstrate the associative property for integers?

1. $\left(a\right)+\left(b\right)+\left(c\right)=a+b+c$
2. $(a+b)+c=a+b+c$
3. $(a+b)+c=a+(b+c)$
4. $\left(abc\right)+d=a+\left(bcd\right)$

Q. $\text{Sum of}n\text{consecutive odd numbers is divisible by}n.\text{Explain the reason.}$
[3 marks]

Q. What is the smallest square number that is divisible by each of the numbers 6, 9 and 15?

1. 920
2. 890
3. 820
4. 900

Q. $\text{Find the sum of integers from 1 to 50 which are divisible by 2.}$
[3 marks]

Q. The collection of all natural numbers less than 10, 000 forms a set.

1. True
2. False

Q. If $P=5^{33}+5^{33}+5^{33}+5^{33}+5^{33}$ and $Q=3^{33}+3^{33}+3^{33}$ and $PQ={15}^x$, then x equal to

1. 32
2. 35
3. 30
4. 34

Q. How many six digit numbers can be formed using the digits $0,1,2,3,4,5$?

Q. The collection of all natural numbers less than 10, 000 forms a set.

1. False
2. True

Q.

Find the value of
$\left[\right(3+4–6÷2+2)+(9÷3+6\times 5)÷11].$

1. 11

2. 5

3. 9

4. 8

Q. The value of (101)${}^2$ is

1. 103001
2. 10201
3. 10301
4. 102001

Q.

Fill in the boxes with correct symbol out of $>,$ $=,$ or $<:$

$-1\_\_\_\_\_\frac{5}{-5}$

Q. The sum of the first n consecutive natural numbers is a number.

1. negative
2. square
3. triangular
4. cubic

Q. Rita: You are 6 years older than me.
Ram: Yes, and after a year, I’ll be twice as old as you.
If x represents the present age of Rita, find the correct equation representing this scenario.

1. 2(x + 7) = x + 1
2. x + 6 = 2x
3. x + 7 = 2x + 1
4. x + 7 = 2(x + 1)

Q. How many integers are there between 100 and 200 that are divisible by both 6 and 9?

Q. If $a$ and $b$ are two odd positive integers such that $a>b$, then prove that one of the two numbers $\frac{a+b}{2}$ and $\frac{a-b}{2}$ is odd and the other is even.

Q. If ${18}^3$ is expressed as the sum of consecutive odd numbers, then the sum of the first and the last term will be ______.

Q. Use the formula : $(a+b)(a-b)=a^2-b^2$ to evaluate :
$7.7\times 8.3$

Q. When $1!+2!+3!+.........+25!$ is divided by $7$, what will be the remainder

1. $0$
2. $5$
3. $1$
4. None of the above

Q. Rajesh travels 2/5 of his journey by car , 1/4 of his journey by bus and remaining 210 km by train . What is total length of journey

Q. What is the smallest square number that is divisible by each of the numbers 6, 9 and 15?

1. 920
2. 890
3. 820
4. 900

Q. Find three consecutive even integers such that the second is half of the sum of first and the third integer.