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 1002 − 992 - 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

1002 − 992

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

Using this formula, we get:
(i) 1002 − 992   = (99 + 1) + 99
= 199

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 3 Squares and Square Roots
Exercise 3.2 | Q 6.1 | Page 19