Advertisements
Advertisements
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
1112 − 1092
Advertisements
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 − 1102 + 1102 − 1092
= (111 + 110) + (110 + 109)
= 440
APPEARS IN
RELATED QUESTIONS
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
Observe the following pattern
\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) = \frac{2 \times 3 \times 4}{3}\]
\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) = \frac{3 \times 4 \times 5}{3}\]
\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) + \left( 4 \times 5 \right) = \frac{4 \times 5 \times 6}{3}\]
and find the value of(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)
Find the square of the following number:
425
Find the square of the following number:
575
Find the square of the following number:
512
If one member of a pythagorean triplet is 2m, then the other two members are ______.
The hypotenuse of a right triangle with its legs of lengths 3x × 4x is ______.
The sides of a right triangle whose hypotenuse is 17 cm are ______ and ______.
Write the Pythagorean triplet whose one of the numbers is 4.
The dimensions of a rectangular field are 80 m and 18 m. Find the length of its diagonal.
