Page 110 - Mathematics_Form_3

Sequences and series

11. If the sum of the first 8 terms of a GP Therefore, the geometric mean is ± 4.
is 2 ,S where S is the sum of the The geometric series can either be
4
4
first 4 terms, find the common ratio.
2 + 4 + 8 + ··· or 2 – 4 + 8 – ···
12. If the second and fourth terms of a
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geometric progression are 7.2 and
5.832, respectively. Find; Example 4.25

(a) the common ratio
The geometric mean of 12 and x is 6.
(b) the first term Find the value of x.

(c) the sum of the first fifty terms, Solution
giving your answer to three Given M = 6 and one term = 12, then
decimal places _
M = ± √ ab
_

6 = ± √ 12x
Geometric Mean
If a, M , and b are three consecutive terms 36 =12 x

of a geometric progression, then M is x = 3
called the geometric mean of a and b. Therefore, the value of x is 3.
The common ratio of the GP is

M
b __
r = = . Thus,
__
a
M
Example 4.26
M
= gives,
b __
__
a
M
_ Find the geometric mean of − 64
2
M = ab ⇒ M = ± √ ab
and − 289 and write down its
Therefore, the geometric mean of a and geometric series.
_
b is M = ± √ ab .
Solution
_

From M = ± √ ab , it implies that,
Example 4.24
×−
−
Find the geometric mean of 2 and 8, M = ± ( 64) ( 289) Mathematics for Secondary Schools
hence write down its geometric series. = ± 18496
Solution = ± 136
_
From M = ± √ ab , where a = 2 and b = 8,
Therefore, the geometric mean is ± 136.
it follows that
_ The geometric series can be either
M = ± √ 2 × 8
_ –64 + 136 – 289 + · · · or
= ± √ 16
–64 – 136 – 289 – · · ·
= ± 4
Student\s Book Form Three 103

18/09/2025 09:59:26
MATHEMATIC F3 SB.indd 103
MATHEMATIC F3 SB.indd 103 18/09/2025 09:59:26