Question

Write each of the following numbers as difference of the square of two consecutive natural numbers. (a) 49

(b) 75
(c) 125

Answer 1

Explanation:

Solution :-

A series of whole numbers that follow one another consecutively and without any breaks are known as consecutive natural numbers. To put it another way, when you list a series of natural numbers, each one is one unit bigger than the one before it. Natural numbers are ordered starting at 1, and each additional number is created by adding 1 to the previous number.

The initial few consecutive natural numbers, for instance, are:

1, 2, 3, 4, 5, 6, ...

(a) 49:

25² - 24²=625-576=49

(b) 75:

19² - 18²=361-324=75

(c) 125:

63² - 62²=3969-3844

Answer 2

Sure, here are the numbers expressed as differences of the squares of two consecutive natural numbers:

(a) 49:

49 = 25² - 24²

(b) 75:

75 = 19² - 18²

(c) 125:

125 = 64² - 63²

In each case, the difference of the squares of two consecutive natural numbers results in the given number.