Observe the following pattern
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

(i) 1002 − 992

(ii) 1112 − 1092

(iii) 992 − 962

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

(ii) 1112 − 1092 = 1112 − 110+ 1102 − 1092

= (111 + 110) + (110 + 109)

= 440

(iii) 992 − 962 = 992 − 98+ 98− 972 + 97− 962

= 99 + 98 + 98 + 97 + 97 + 96

= 585

Administrator

Leave a comment

Please enter comment.
Please enter your name.