General term

Definition

The general term Tₙ of a number pattern is a formula that gives the value of the term in position n. For a linear pattern it has the form Tₙ = bn + c, where b is the constant difference; for a quadratic pattern (Grade 11) it is Tₙ = an² + bn + c.

Worked example

For 2; 7; 12; 17; …, the difference is 5, so Tₙ = 5n + c, and T₁ = 2 gives c = −3: Tₙ = 5n − 3.

Which term of 4; 10; 16; … is 100? Tₙ = 6n − 2 = 100 gives n = 17, the 17th term.

Where it appears in the exam

General term is part of the number patterns section of CAPS Grade 10 Mathematics and is examined in Paper 1 of the November exam.

Step-by-step method

1. Find the constant difference b.
2. Write Tₙ = bn + c.
3. Substitute n = 1 and T₁ to find c.
4. Check the formula with the second term.

Common mistake

Using the first term as c, e.g. writing Tₙ = 5n + 2 for 2; 7; 12; …

Related number patterns terms

• Quadratic sequence

Frequently asked questions

What does general term mean in Grade 10 Maths?

The general term Tₙ of a number pattern is a formula that gives the value of the term in position n. For a linear pattern it has the form Tₙ = bn + c, where b is the constant difference; for a quadratic pattern (Grade 11) it is Tₙ = an² + bn + c.

Which paper tests general term in Grade 10?

General term belongs to the Number patterns section of CAPS Grade 10 Mathematics, which is examined in Paper 1 of the November exam.

How do I practise questions involving general term?

Snap a question that uses general term into Snap&Learn with your grade set to Grade 10, or work through the Grade 10 topic guide and practice papers.