Foundation and Higher · the nth term
Find the nth term
of a sequence.
Two steps.
the difference tells you
the times table
one rule for every position —
nth term
n is the position in the sequence
the rule turns position into term
step 1 of 4
Find the difference
1. Find the gap between the terms: + 3.
2. Up in 3s: think of the 3 times table.
✓ The rule starts 3n
step 2 of 4
Compare with 3, 6, 9…
1. Write 3n above: 3, 6, 9, 12.
2. The sequence is always 2 more.
✓ nth term = 3n + 2
3n: the 3 times table
the sequence
step 3 of 4
Check it
1. Test the first term and one other.
2. Both match the sequence.
✓ Ten seconds that saves the marks
nth term = 3n + 2
n = 1: 3 × 1 + 2 = 5
n = 4: 3 × 4 + 2 = 14
matches 5, 8, 11, 14
step 4 of 4
Going down
1. Down in 4s: the rule starts −4n.
2. From −4 up to 20 is + 24.
✓ Also written 24 − 4n
−4n: −4, −8, −12 + 24 to match
nth term = −4n + 24
finding the nth term —
Difference
gives the number in front of n
Compare
times table against the sequence
Check
try n = 1 and one more
A common slip: writing n + 3.
Going up in 3s means 3n.
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