Prove that the difference of the square of two consecutive odd numbers is always a multiple of 8. [OCR GCSE June 2017 Paper 5]

Part 1 of this question asks you to explain why 2n+1 is an odd number, so it is assumed that the student knows this already. The definition of any odd number is 2n+1. Since all consecutive odd numbers are two values apart, the next consecutive odd number is defined as 2n+3 (for all n). The square of the equations are: (2n+1)2=4n2+4n+1 (2n+3)2=4n2+12n+9. Then to find the difference we must subtract one equation from the other. It doesn't matter which way round you do this, the result will be ±(8n-8) = ±8(n-1). This solution shows that no matter what n is, it is being multiplied by 8: the result (the difference of the square of two consecutive odd numbers) is therefore always a multiple of 8.

Answered by Jon J. Maths tutor

8643 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Find the points of intersection of the line y+x=8 and a circle with centre at (3,-2) and radius 5.


Solve the simultaneous equations x^2 + y^2 = 9 and x+ y = 2. Give your answer to 2.d.p


Solve the simultaneous equations. 5x+y=21, x-3y=9.


Solve algebraically the simultaneous equations: 6m + n = 16 and 5m - 2n = 19


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences