Page 103 - Mathematics_Form_3

Sequences and series

Example 4.15 (c) 5 5 and 65

2
Find the arithmetic mean of 3 and 27. (d) (K − M) and K − M
2
2
Solution (e) − 3 and + 3
Given a = 3, b = 27.
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(f) − 7 and 9
a + b
_
Arithmetic mean, M =
2 2. The arithmetic mean of two
______
M = 3 + 27 numbers is 25. If one of the

2 numbers is 30, find the other
30
___
= number.
2
3. Three numbers are in AP. If their
= 15 sum is 27 and the sum of their
Therefore, the arithmetic mean is 15. squares is 261, find the numbers.
4. Find three terms of an arithmetic
Example 4.16 progression with the arithmetic
mean of 20 and whose sum is 60.
An arithmetic mean and one of the
terms of an arithmetic progression are 5. The arithmetic mean of three
14 and 7, respectively. Find the other consecutive odd numbers in AP
term. is 21. Find the numbers.

Solution 6. The numbers 24, m, y, and 72
Let the terms be a and b. are such that m is the arithmetic
a + b mean of 24 and y, while y is the
Arithmetic mean, M = _

2 arithmetic mean of m and 72.
Given M = 14 and a = 7: Required b Find the values of m and y.
Mathematics for Secondary Schools Exercise 4.5 Geometric Progression (GP)
7 + b
_

Thus, 14 =
2
28 = 7 + b

b = 21
In everyday life, geometric progressions
Therefore, the other term is 21.
occur in scenarios such as population
growth or decay, for which the population
may increase or decrease during a
1. Find the arithmetic mean of the
Engage in Activity 4.4 to formulate the
following: specific period of time.
general concept of a GP to determine
(a) 2 2 and 28
_ _ the amount of money saved for a certain
(b) 2 − √ 3 and 2 + √ 3 period.

96 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 96
MATHEMATIC F3 SB.indd 96 18/09/2025 09:59:23