How do you find the nth term of an arithmetic sequence?

Use a + (n − 1)d, where a is the first term and d is the common difference.

Sequences · Grades 11–11

Sequences Worksheets

Are you adding the same number each time, or multiplying by it? That one question sorts arithmetic from geometric. Worksheets for next-term and nth-term.

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What it is

A sequence follows a rule. Arithmetic sequences add the same number (the common difference) each term; geometric sequences multiply by the same number (the common ratio).

Why it matters

Sequences and series model growth, patterns, and sums across algebra, finance, and calculus, and they train students to find and apply a rule.

How to do it

Find the rule: subtract consecutive terms (difference) or divide them (ratio).
For the next term, apply the rule once more.
For the nth term of an arithmetic sequence, use a + (n − 1)d.

Examples by level

Beginner1, 3, 5, 7, __ =9
Intermediate2, 6, 18, 54, __ =162
AdvancedFind the 10th term: 3, 8, 13, … =48

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

Confusing arithmetic (add) with geometric (multiply).
An off-by-one on n − 1 when finding the nth term.
Adding the common ratio instead of multiplying by it.

Tips

Arithmetic adds; geometric multiplies.
For the nth term, remember it's (n − 1) steps from the first term.

For parents

Ask: are you adding the same number each time (arithmetic) or multiplying by the same number (geometric)?

For teachers

Have students write the common difference or ratio between each pair of terms before extending the sequence.

Key vocabulary

common difference: the constant added in an arithmetic sequence
common ratio: the constant multiplied in a geometric sequence

Frequently asked questions

What is the difference between arithmetic and geometric sequences?: Arithmetic sequences add a constant (the common difference) each term; geometric sequences multiply by a constant (the common ratio).
How do you find the nth term of an arithmetic sequence?: Use a + (n − 1)d, where a is the first term and d is the common difference.

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