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WEEK 3:
TOPIC: Sequence and Series 1
Content:
- Meaning and types of sequence.
- Example of an A. P.
- Calculation of: (i) first term (ii) common difference (iii) nth term (iv) Arithmetic mean (v) sum of an A. P.
- Practical problems involving real life situations.
Meaning and types of sequence
SEQUENCES:
A sequence is an ordered list of numbers whose subsequent values are formed based on a definite rule. The numbers in the sequence are called terms and these terms are normally separated from each other by commas.
Examples:
2, 4, 6, 8, 10,……
Rule: Addition of 2 for subsequent terms.
70, 66, 62, 58, 54,……
Rule: Subtraction of 4 for subsequent terms.
3, -6, 12, -24,……
Rule: Multiply each term by –2.
There are many types of sequences. We shall be considering the Arithmetic Progression and Geometric progression.
Finite and Infinite Sequences
A finite sequence is a sequence whose terms can be counted. i.e. it has an end. These types of sequences are usually terminated with a full stop. e.g. (i) 3,5,7,9,11,13. (ii) -7,-10,-13,-16,-19,-21.
If however, the terms in the sequence have no end, the sequence is said to be infinite. These types of sequences are usually ended with three dots, showing that it is continuous. e.g. (i) 5,8,11,14,17,20… (ii) -35,-33,-31,-29,-27,…
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