Question

Three consecutive odd numbers have a sum of 45. What is the greatest number?

Answer 1

The greatest odd number is `17`

Explanation:

Let the three consecutive odd numbers are `2n+1,2n+3 and 2n+5`

Their sum is `(2n+1)+(2n+3)+(2n+5)=45 or 6n+9=45 or 6n=36 or n=6`

The greatest odd number is `2n+5=2*6+5=17`[Ans]

Answer 2

Slightly different start point but gives the same answer.

17

Explanation:

You do not need to define a sequence that guarantees you are looking at odd numbers.

However, you must guarantees they are all of same type. That is all odd or all even.

You do this as follows

Let the first number be `n`
Then the next number of same type (odd or even) is `n+2`
The number after that is `n+4`

So we have:

`n+(n+2)+(n+4)=45`

`3n+6=45`

`3n=39`

`n=39/3=13`

So the greatest number is `n+4" "=" "13+4" "=" "17`