Foundation and Higher · sequences
Sequences.
Two kinds of rule.
Know which you have.
term to term,
or straight to any term
each number in a sequence is a —
Term
term-to-term: how to get the next one
nth term: jump to any position
rule type 1
Term to term: add
1. How do you get to the next term?
2. Keep doing it to continue the sequence.
✓ Give the start and the rule
start at 5, add 3 each time
5
+ 3
8
+ 3
11
+ 3
14
+ 3
17
+ 3
20
rule type 1
Term to term: multiply
1. The gaps are 4, 12, 36: not the same.
2. So try multiplying: each term is × 3.
✓ 54 × 3 = 162
start at 2, multiply by 3
rule type 2
The nth term rule
1. n is the position: 1st, 2nd, 3rd…
2. Substitute n = 1, 2, 3 for the first terms.
✓ 4n goes up in 4s
nth term = 4n + 1
n = 1: 4 × 1 + 1 = 5
n = 2: 4 × 2 + 1 = 9
n = 3: 4 × 3 + 1 = 13
5, 9, 13, …
rule type 2
Jump to any term
1. No need to list 50 terms: substitute 50.
2. To test a number, set the rule equal to it.
✓ A term needs a whole-number n
50th term: 4 × 50 + 1 = 201
Is 82 a term? 4n + 1 = 82
4n = 81, so n = 20.25
not a whole number: no
two kinds of rule —
Term to term
start number and what to do
nth term
substitute the position
Is it a term?
solve for n: whole number?
Term to term: the next few.
nth term: any term you like.
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