Sum of the First n Odd Natural Numbers Is Equal to n Squared

Q.

The sum of two consecutive odd numbers is 56. Find the numbers

Q.

The GCD of x³-x²+x-1 and x⁴-1 is _____________.

1. (x+1) (x-1)

2. x²+1

3. (x-1) (x²+1)

4. (x+1) (x²+1)

Q.

The sum of 5 consecutive odd numbers is 135. Find the numbers.

Q.

The sum of first 16 odd numbers is:

1. 296

2. 286

3. 256

4. 246

Q. What is the sum of the first 9 odd natural numbers ?

1. 91
2. 81
3. 61
4. 101

Q. Can you solve this? _ +_ +_= 30. Fill the boxes only using , (1, 3, 5, 7, 9, 11, 13, 15)

Q.

Let A = {x such that x belongs to N and x+1 < 8} and B = {x such that x belongs to N and x+3≤5}. Then find A union B?

Q.

Question 12

Write the correct answer from the given four options.

The sum of first n odd natural numbers is

a) $2n+1$
b) $n^2$
c) $n^2-1$
d) $n^2+1$

Q. What is the sum of the odd natural numbers 1, 3, 5, 7 and 9 ? (Use the formula ).

1. 25
2. 14
3. 16
4. 39

Q. 2^1990 / 1990

Q. is the number of steps to reduce 169 to 0 by the method of repeated subtraction.

1. 9
2. 11
3. 13
4. 15

Q.

Question 62

State whether the following statement is true or false:

The sum of first n odd natural numbers is $n^2$.

Q. 1+a+b+ab

Q. How many consecutive odd numbers will be needed to obtain the sum as 18³?

Q.

The GCD of 90x²y³, 15x⁴y and 15y³ is

1. 30y

2. 15xy

3. 30xy

4. 15y

Q. Express 49 as the sum of 7 odd nos. Write the formula how you do that.

Q. 1 + 3 + 5 +...+ 51 = ?

1. 576
2. 676
3. 276
4. 476

Q. The sum of first 5 consecutive odd numbers is equal to 25.

1. True
2. False

Q. The square roots of two numbers x, y are 25 and 12. It is given that x < y. Choose the correct options.

1. $\sqrt{x}$ = 12
2. $\sqrt{x}$ = 25
3. $\sqrt{y}$ = 12
4. $\sqrt{y}$ = 25

Q. If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
(a)

(b)

(c)

(d)

Q.

Find the number of steps to reduce 169 to 0 by the method of repeated subtraction.

1. 9
2. 15
3. 11
4. 13

Q. What is the sum of successive odd natural numbers?

1. 0
2. n / n
3. n + n
4. n x n

Q. The sum of first 12 odd numbers is 144.

1. False
2. True

Q. There will be 2n natural numbers between $n^2$ and $(n+2{)}^2$

1. False
2. True