quadratic nth term using factors

this is an idea for working on quadratic sequences, developed with Martin Wilson in Harrogate

we hope that students will be able to make a link between factorising numbers and factorising a quadratic expression

the powerpoint is here

the technique involves

• transforming a given sequence by adding or subtracting a number to/from all of the terms, this number chosen so that all of the resulting terms have factor pairs
• seeing if this provides a regular growing (or decreasing) pattern
• if not, looking at another option

this approach might precede an algebraic one (outlined here)

three GCSE exam board questions set this summer (2017) are explored, one that can be factored without transformation