Math # What is the sum of 10 consecutive numbers from 31?

Let N denote the smaller of the two natural numbers. Since the two numbers are consecutive, the larger natural number = N+1.

Given, Sum of the two numbers = 31

i.e., N+N+1 = 31

Or, 2N + 1 = 31

Subtracting 1 from both sides,

2N+1–1 = 31–1

Or, 2N = 30

Dividing both sides by 2,

2N/2 = 30/2

Or, N = 15

Difference of the squares of the two numbers

=(N+1)² - N² = N² + 2N + 1 - N² = 2N + 1

= 2 x 15 +1 (Substituting for N = 15 from (1))

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