Question

Given that m is an integer,
(a) write down expressions for the next two odd numbers after 2n - 1,
b) © find, in its simplest form, the expression for the sum of these three odd numbers,
(©) explain why the sum is a multiple of 3,
(c) find, in its simplest form, an expression for the sum of the squares of these three odd
numbers.

Answer 1

a) they would have to be 2 units apart, so:
2n-1, 2n+1, 2n+3

b) sum of those = 2n-1 + 2n+1 + 2n+3 = 6n +3
we can factor out 3 to get 3(2n+1) which is a multiple of 3, since 3 is a factor

c) sum of squares = (2n-1)^2 + (2n+1)^2 + (2n+3)^2
= 4n^2 - 4n + 1 + 4n^2 + 4n + 1 + 4n^2 + 12n + 9
= 12n^2 + 12n + 11