Answer

Verified

382.5k+ views

**Hint**: Here, we are given a pattern and based on that pattern we need to find the value for $ {100^2} - {99^2} $ . Now, this is a logical question, so to find the value of $ {100^2} - {99^2} $ , we need to find the logic behind this pattern. The logic behind this pattern is that the difference of the squares of two consecutive numbers is equal to the sum of these numbers. Using this logic, we are going to find the value of $ {100^2} - {99^2} $ .

**:**

__Complete step-by-step answer__In this question, we are given a pattern and based on that pattern we need to find the value of $ {100^2} - {99^2} $ .

The given pattern is:

$

{2^2} - {1^2} = 2 + 1 \\

{3^2} - {2^2} = 3 + 2 \\

{4^2} - {3^2} = 4 + 3 \\

{5^2} - {4^2} = 5 + 4 \;

$

Now, this is a logical question, and to find the value for $ {100^2} - {99^2} $ , we need to understand the logic behind the given pattern and then use that logic to find the required answer.

Let us find the logic behind the given pattern.

Here, we can see that the square of the number being subtracted is written on right is smaller than the square of number written on right and the result is given by their addition.

That means the logic behind this pattern is that when we subtract the squares of two consecutive numbers, where the smaller number is subtracted from the bigger number, the answer will be the sum of these consecutive numbers.

$ {2^2} - {1^2} = 2 + 1 $ : The difference of squares of two consecutive numbers $ \left( {{2^2} - {1^2}} \right) $ is equal to the sum of these consecutive numbers $ \left( {2 + 1} \right) $ .

$ {3^2} - {2^2} = 3 + 2 $ : The difference of squares of two consecutive numbers $ \left( {{3^2} - {2^2}} \right) $ is equal to the sum of these consecutive numbers $ \left( {3 + 2} \right) $ .

$ {4^2} - {3^2} = 4 + 3 $ : The difference of squares of two consecutive numbers $ \left( {{4^2} - {3^2}} \right) $ is equal to the sum of these consecutive numbers $ \left( {4 + 3} \right) $ .

$ {5^2} - {4^2} = 5 + 4 $ : The difference of squares of two consecutive numbers $ \left( {{5^2} - {4^2}} \right) $ is equal to the sum of these consecutive numbers $ \left( {5 + 4} \right) $ .

Hence, according to this logic, the answer of $ {100^2} - {99^2} $ will be equal to the sum of the numbers that is 100 and 99. Therefore,

$ \Rightarrow {100^2} - {99^2} = 100 + 99 = 199 $

**So, the correct answer is “199”.**

**Note**: Let us find these answers using the normal method and see if we are correct or not.

$

{2^2} - {1^2} = 4 - 1 = 3 = 2 + 1 \\

{3^2} - {2^2} = 9 - 4 = 5 = 3 + 2 \\

{4^2} - {3^2} = 16 - 9 = 7 = 4 + 3 \\

{5^2} - {4^2} = 25 - 16 = 9 = 5 + 4 \;

$

Therefore,

$ \Rightarrow {100^2} - {99^2} = 10000 - 9801 = 199 = 100 + 99 $

Hence, our answer is correct.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Who was the Governor general of India at the time of class 11 social science CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference Between Plant Cell and Animal Cell