Let n be an integer, so that 2n+1 is an odd number. - Write down, in terms of n, the next odd number

Question

Let n be an integer, so that 2n+1 is an odd number. - Write down, in terms of n, the next odd number after 2n+1. - Show that the difference between the squares of two consecutive odd numbers is always a multiple of 8. - Hence, without using a calculator, find the value of 10012-9992.

Accepted Answer

(a) $2n+3$ (b) $(2n+3)^2-(2n+1)^2=8(n+1)$ (c) $4000$

Squares of consecutive odd numbers

Squares of consecutive odd numbers

Solution:

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