Mathematics

Grade-8

Easy

Question

# Which of the following is the difference between the squares of two consecutive natural numbers?

- Sum of the two numbers
- Difference of the numbers
- Twice the sum of the two numbers
- Twice the difference between the two numbers.

Hint:

### 1. Let the 2 consecutive natural numbers be x & x+1.

2. (a + b)^{2} = a^{2} + 2ab + b^{2}

## The correct answer is: Sum of the two numbers

### TO FIND-

Difference between squares of 2 consecutive natural numbers.

SOLUTION-

Let the first natural number be x

∴ next consecutive natural number = x + 1

Now, we are given that-

(x + 1)^{2} - (x)^{2}

= [x^{2} + (2 * x * 1) + 1] - x^{2}

= x^{2} + 2x + 1 - x^{2}

= 2x + 1

From the given options,

a. 2 [x + (x + 1)] = 2 (x + x + 1) = 2 (2x + 1) = 4x + 2

b. x + (x + 1) = x + x + 1 = 2x + 1

c. (x + 1) - (x) = x + 1 - x = 1

d. 2 [(x+1) - x] = 2 (x + 1 - x) = 2 * 1 = 2

From the above calculations , we observe that-

Difference between the squares of 2 consecutive numbers = Sum of 2 consecutive numers = 2x + 1

FINAL ANSWER-

Option 'b' i.e. 'Sum of the two numbers' is the correct answer to the given question.

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