Question

You can represent an odd integer whith the expression 2n+1, where n is any integer . Write and solve an equation to find three consecutive odd that have a sum of 63

Answer 1

Any odd number can be expressed by 2n+1.

For example,

2n+1=111
2n=110
n=110/2=55

means that 111 is 2n+1 for n=55


Thus if an odd number is 2a+1, the next few numbers are as follows:

2a+1, 2a+2, 2a+3, 2a+4, 2a+5

So 2a+1, 2a+3 and 2a+5 are 3 consecutive odd numbers.


Back to our problem:

three consecutive odd numbers whose sum is 63 are:

(2n+1)+(2n+3)+(2n+5)=63

6n+9=63

6n=63-9=54

n=54/6=9


2n+1=2*9+1=18+1=19, the 2 next odd numbers are 21 and 23


Answer: 19, 21, 23