Prove that the sum of 6 consecutive odd numbers is an even number?
Please see below.
Any two consecutive odd numbers add up to an even number.
Any number of even numbers when added result in an even number.
We can divide six consecutive odd numbers in three pairs of consecutive odd numbers.
The three pair of consecutive odd numbers add up to three even numbers.
The three even numbers add up to an even number.
Hence, six consecutive odd numbers add up to an even number.
Let first odd number be
Six consecutive odd numbers are
Sum of these six consecutive odd numbers is
Adding by brute force method
We see that first term will always be even
An odd number has the form
Let be the first
We know also that the sum of n consecutive numbers in a arithmetic progresion is
which is an even number for every