Find a term
Find the tenth term of 4, 7, 10, … .
- The first term is 4 and the difference is 3.
- There are nine changes before the tenth term: 4 + 9 × 3.
Answer: 31
Arithmetic sequences and sums
Find the nth term and the sum of the first n terms of an arithmetic sequence.
Before you start
You’ll need Rearranging formulae. Follow a link if you want to revise it first.
Counting the steps between terms
An arithmetic sequence has a constant difference d, including when d is negative.
The nth term is a + (n − 1)d: reaching the first term requires no changes.
The sum of n terms is n(a + last)/2, pairing the first and last terms. It is not the same as the nth term.
For the sequence below, the tenth term is 31, while the first ten terms add up to 175.
A term and a total
Find a sum
Find the sum of the first ten terms of 4, 7, 10, … .
- The last term is 31.
- Pair the ends, or use 10(4 + 31)/2.
Answer: 175
Using a + nd counts one extra change.
Practice questions
The first link uses smaller values. Move on when you can answer without referring to the examples. The difficulty settings aren’t tied to exam grades.
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Check your understanding
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How does the term formula change for a decreasing sequence?