# The difference of the squares of two consecutive numbers is their sum. Is the given statement true or false

**Solution: **

The statement ‘The difference of the squares of two consecutive numbers is their sum’ is true.

Let n and n+1 be the two consecutive numbers. Their sum = n+1 +n = 2n +1

(n+1)^{2} - n^{2} = n^{2} + 2n+ 1^{2 }- n^{2 }= 2n +1

Thus proved.

**✦ Try This: **Is 100^{2} - 99^{2 }= 199?

Let us consider two consecutive numbers 99 and 100.

Now, let us consider difference of the square of these two consecutive numbers,

Using standard identity : a^{2} - b^{2} = (a + b) (a - b)

Here, a = 100 and b = 99,

100^{2} - 99^{2 }= (100 + 99) (100 - 99)

= (199) (1)

= 199

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 9

**NCERT Exemplar Class 8 Maths Chapter 7 Problem 75**

## The difference of the squares of two consecutive numbers is their sum. Is the given statement true or false

**Summary:**

The statement ‘The difference of the squares of two consecutive numbers is their sum’ is true

**☛ Related Questions:**

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