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Observe the Following Pattern 22 − 12 = 2 + 1 32 − 22 = 3 + 2 42 − 32 = 4 + 3 52 − 42 = 5 + 4 and Find the Value of 1112 − 1092 - Mathematics

Observe the following pattern
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of 

 1112 − 1092

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Solution

From the pattern, we can say that the difference between the squares of two consecutive numbers is the sum of the numbers itself.
In a formula: 

`(n+1)^2-(n)^2=(n+1)+n`

 1112 − 1092 = 1112 − 110+ 1102 − 1092
                        = (111 + 110) + (110 + 109)
                        = 440

Notes


 

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 3 Squares and Square Roots
Exercise 3.2 | Q 6.2 | Page 19
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