Question

Find three consecutive odd numbers whose sum is 1701.

Answer 1

565, 567, 569

Explanation:

let 'n' be an odd integer, then (n + 2) is the next odd interger, and (n + 4) is the third consecutive integer.

Ex: If 3 is our first, then 5, followed by 7

3 + 2 = 5,

3 + 4 = 7

So we have

n + (n + 2) + (n + 4) = 1,701

Now simplify and solve for n

n + n + 2 + n + 4 = 1,701 (we can drop the parenthesis)

3n + 6 = 1,701 (combine like terms)

3n = 1,695 (subtract 6 from both sides to isolate the n term)

n = 565 (divide both sides by 3 to isolate n)

n = 565

n + 2 = 567

n + 4 = 569