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

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
= [x² + (2 * x * 1) + 1] - x²
= x² + 2x + 1 - x²
= 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.