Sequences and series Grade 11

Sequences and series is the second grade 11 mathematics topics, which may also be used by other people, especially the grade 12 students, GCE candidates, the college students and teachers who need references.

Don’t forget to consult the pastpapers for more and advanced exercises

LEARNING OBJECTIVES

At the end of this chapter you should be able to:

• Identify an arithmetic progression (AP)
• Find the nth term of the AP
• Find the sum of an AP
• Find the arithmetic mean
• Identify a geometric progression (GP)
• Find the nth term of a GP
• Find the geometric mean
• Find the sum of a geometric progression
• Find the sum to infinity of a Geometric progression

KNOWLEDGE:

• Arithmetic and Geometrical Progressions.
• The nth terms of AP and GP
• Sums of APs and GPs
• Arithmetic and geometric means
• Sum to infinity of a Geometric progression

 SKILLS

• Identification of arithmetic and geometrical Progressions.
• Ordering of Arithmetic and Geometrical Progressions.
• Computation of Arithmetic and Geometrical Progressions.

VALUES

• Accuracy in computing progressions.
• Appreciation of the nth term of the progression.
• Prediction of the nth term.

CROSSCUTTING ISSUES

Life skills: Sequences and series are applied in computing

Gender balance.

Sequences and series meaning

A sequence is an ordered list of numbers.  The sum of the terms of a sequence is called a series.

The sequence 2, 4, 6, 8 … is the sequence of even numbers and to continue the sequence the rule (or pattern) is add two.

A sequence is a list of numbers arranged in a definite order. The numbers in a sequence are called “terms”. For example 10, 20, 30, 40, 50 is a sequence arranged in such way that each term is equal to the preceding term plus 10.

A sequence can be finite (5, 10, 15, 20) or infinite (1, 3, 5, 7,……….); it can also be given as a formula a_n where a_n denotes n^th term.