Question

Determine whether the following statement is sometimes, always, or never true. Explain your reasoning.

The sum of three consecutive odd integers equals an even integer.

Short answer

The statement is never true.

Step-by-step solution

Step 1. Sum of two odd integers.

The sum of two odd numbers will always be an even number.

For example, Sum of 3 and 5 is 8.

Step 2. Sum of three odd integers.

If three odd integers are added together, the sum is always odd because the first two odd numbers will always sum to an even number, and the sum of this even number and the third odd number will always be odd.

Step 3. Few examples.

$\begin{array}{l}3+5+7=15\\ 7+9+11=27\end{array}$

Hence, the statement is never true.