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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
RELATED QUESTIONS
What will be the units digit of the square of the following number?
977
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
992 − 962
Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
12 + 22 + 32 + 42 + ... + 102
Which of the following number square of even number?
121
Which of the following number square of even number?
225
Which of the following number square of even number?
4489
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
54
Find the squares of the following numbers using diagonal method:
171
Find a Pythagorean triplet in which one member is 12.
Find the area of a square field if its perimeter is 96 m.
