Question

Find three consecutive odd numbers whose sum is 1899.

Answer 1

631, 633, 635

Explanation:

Odd numbers exists in AP with common difference of 2.

That is; 1, 2, 5, 7 etc

So lets say the middle number of the three consecutive numbers is x, the next number to it Will be (x+2), and the previous number will be (x-2)

Therefore, the sequence is (x-2), x, (x+2) ... (1)

and the series will be, (x+

-2) + x + (x+2) = 1899

Solve for x;

x + x + x - 2 + 2 = 1899

3x + 0 = 1899

x = 1899 ÷ 3

x = 633

Therefore the consecutive odd numbers (following 1) is: (633 - 2), 633, (633+2) = 631, 633, 635