Arithmetic sequence

Definition

An arithmetic sequence increases or decreases by adding the same constant value d to each term. Its general term is Tₙ = a + (n − 1)d.

Worked example

3; 7; 11; 15 … has a = 3 and d = 4, so T₁₀ = 3 + 9(4) = 39.

Find n if the sequence 3; 7; 11; … ends at 199: 199 = 3 + (n − 1)(4), so n − 1 = 49 and n = 50.

Where it appears in the exam

Paper 1 sequences questions ask for a specific term, the number of terms, or the sum Sₙ = n/2[2a + (n − 1)d].

Step-by-step method

1. Confirm the first difference is constant: d = T₂ − T₁.
2. Identify a = T₁.
3. Substitute into Tₙ = a + (n − 1)d.
4. Solve for the unknown term or for n.

Common mistake

Using n instead of (n − 1) in the general term.

Related sequences terms

• Geometric sequence
• Convergence
• Sigma notation

Frequently asked questions

What does arithmetic sequence mean in Grade 12 Maths?

An arithmetic sequence increases or decreases by adding the same constant value d to each term. Its general term is Tₙ = a + (n − 1)d.

Which NSC paper tests arithmetic sequence?

Arithmetic sequence belongs to the Sequences section of CAPS Grade 12 Mathematics, which is examined in Paper 1.

How do I practise questions involving arithmetic sequence?

Snap a question that uses arithmetic sequence into the Snap&Learn AI solver, or work through the sequences topic guide and NSC past papers.