don steward
mathematics teaching 10 ~ 16

Sunday, 10 April 2016

generalising GCSE questions (15)

an AQA question about finding nth term values for numbers that are in two (linear) sequences

a more general question might be: what numbers are in the (infinite) sequences
2n + 1 and
3n - 1?

other 'overlapping' sequences can be explored

some don't have an overlap - when?

some examples

a rule for finding the coefficient of 'n' for the 'overlap' sequence (12 in the above examples) is reasonably easy to discern

a rule for the constant term in the expression is slightly more difficult to sort out

it needs to be appreciated that an infinite linear sequence (indicated by ...) has an infinity of general (nth terms)
e.g. the nth term rules: 3n - 1 and 3n + 2 and 3n + 5 and 3n - 4 etc. all give the same (infinite) sets of numbers
they just start in different places

for the given nth term rules, create other nth term rules that give the same sequence of numbers

any of the common constant terms of the two expressions can form the constant term of the 'overlap' nth term rule

e.g. the nth term for the overlap of nth term sequences 3n - 2 and 4n + 1 is        12n + 13 or 12n - 11 or...

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