SS1 Second Term Further Mathematics Lesson Note – Sequences

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WEEK 1

CLASS: SS1

TOPIC:   SEQUENCES

CONTENT:

1. Sequences and Types.
2. Arithmetic progression
3. Geometric progression

Sub – Topic: SEQUENCE AND TYPES

A sequence is a succession of terms generated according to some rules or laws. Examples are: (a) 1, 3, 5, 7 …. (b) 2, 4, 6, 8, 10, … (c) 2, 4, 8, 16, 32, …  (d) x, x, x², x³, x⁴, x⁵ ……

Every member of each set is called a term. The three dots after each set show that the set of the numbers or terms continues definitely. The terms of a sequence are sometimes called elements of the sequence. When the number of terms in a sequence is limited, the sequence is said to be finite. On the other hand, if the number of elements in a sequence is unlimited or otherwise, the sequence is said to be infinite.

Finite sequences may be specified by listing the elements of the sequence and this list may be complete or incomplete. They can also be specified by a functional relation.

An infinite sequence can also be specified by an incomplete list of its terms or by a functional relation. Sequence (a) above is an example of a finite sequence. It has four terms. The sequences (b), (c) and (d) above are examples of infinite sequences. We may write the terms of a sequence as ₁, ₂, ₃, ₄, …

The general terms or the th term can be designated _k. The th term is _n by this designation.

Example:

1. Given that …….

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