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