Sequences

Study Notes

A sequence is a list of numbers or objects in a special order. A term to term rule allows you to find the next number in the sequence if you know the previous term(s). Example: In the sequence 1, 3, 5, 7,..., add 2 to find the next term. A position to term rule allows you to compute the value of any term. Example: For the sequence 1, 3, 5, 7,..., the nth term is given by $a_n = 2n - 1$. An arithmetic sequence is made by adding the same value each time, called the "common difference". Example: In the sequence 1, 4, 7, 10,..., the common difference is 3.

Exam Tips

Key Definitions to Remember

• A sequence is a list of numbers or objects in a special order.
• A term to term rule helps find the next term using the previous term(s).
• A position to term rule calculates the value of any term in the sequence.
• An arithmetic sequence has a common difference added each time.

Common Confusions

• Confusing term to term rules with position to term rules.
• Forgetting to apply the common difference consistently in arithmetic sequences.

Typical Exam Questions

• What is the next term in the sequence 2, 4, 6, 8, ...? Add 2 to the last term: 10
• What is the 10th term of the sequence defined by $a_n = 3n + 1$? $a_{10} = 3(10) + 1 = 31$
• What is the common difference in the sequence 5, 10, 15, 20, ...? The common difference is 5

What Examiners Usually Test

• Understanding and applying term to term rules.
• Calculating terms using position to term rules.
• Identifying and using the common difference in arithmetic sequences.