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SEQUENCE AND PATTERNS.
Introduction:
We often need to spot a pattern in order to predict what will happen next. In maths, the correct name for a pattern of numbers is called a SEQUENCE. In this topic therefore you will learn how to identify and describe general rules for patterns. You will be able to determine a term in the sequence and find the missing numbers in the sequence.
6.1 Draw and Identify the Patterns
For any pattern it is important to try to spot what is happening before you can predict the next number.
Activity : Identifying the number patterns
(a) 3,6,9,12, . . .
To obtain the next number in the sequence, we add 3 to the previous number. The numbers in this sequence are multiples of 3.
(b) 7,14,21,28, . . .
To obtain the next number in the sequence, we add 7 to the previous number. The numbers in this sequence are multiples of 7.
(c) The table below shows the natural numbers from 1 to 100.
6.1 Exercise Set
6.2 Describing the General Rule.
Activity: Finding the Next Term in the sequence
Find the next numbers in the sequences below.
(a) 3,6,9,12. . .
To obtain the next number in the sequence, we add 3 to the previous number.
(b) 7,14,21,28. . .
To obtain the next number in the sequence, we add 7 to the previous number.
(c) 24,21,18,15. . .
To obtain the next number in the sequence, we subtract 3 from the previous number.
(d) 3,9,27,81. . .
To obtain the next number in the sequence, we multiply 3 with the previous number.
6.2 Exercise Set
6.3 Generating Number Sequence
Activity : Generating a sequence
This involves using a formulae to generate sequences for given values.
EXAMPLES
What sequence do you generate by using the following formula? Take n = 1,2,3,4,5. . .
2n
we substitute the value of n ,in the formula given
2. 8n - 5
we substitute the value of n ,in the formula given
Input/Output machine
Some math problems contain a pattern, so once you find a pattern then you can make a rule that will solve the problem for a given input. Therefore we put numbers into the machine[input], and the machine uses an operation (add, subtract, multiply or divide) to give us a result[output].
EXAMPLES
What number comes out of each of these number machines?
6.3 Exercise Set
6.4 Formulae for General Terms
6.4 Exercise Set
Situation of Integration
There is a family in the neighbourhood of Ushindi Secondary school. The family has a rectangular compound on which they want to put up a hedge.
Support: Physical instruments like hoes, machetes, tape measure.
Resources: Knowledge of construction of figures like rectangles, patterns, sequences.
Task: The family requests you to plant the hedge around their rectangular compound so that it looks beautiful. Explain how you will plant the hedge, making sure that the plants at the corners of the compound are the same in terms of colour
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