Consider the sum of the first n squares: 1+4+9+…+n²

Is the sum odd or even when n is:

a) 66?          b) 92?          c) 101?          d) 123?

Now consider the sum of the first n Fibonacci numbers: 1+1+2+3+5+…+F(n)

[where F(i) is the i^th Fibonacci number]

Is the sum odd or even when n is:

a) 66?          b) 92?          c) 101? 

Consider a series that starts with m-1 odd numbers followed by a single even number. This pattern of m-1 odd, 1 even, repeats indefinitely.

When will the sum of the first n terms be odd? When will it be even?