Page 20 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Chapter 2 Sequences and Series
Geometric mean
If a, b and c are three consecutive terms of a geometric progression, the term b is the geometric mean of a and c.
b
c
The common ratio = — = —
a b
2
∴ b = ac
b = (ac)
The geometric mean of two numbers, p and q, is (pq).

Example 17 2

If (x + 1), 2 2 and (3x – 2) are three consecutive terms of a geometric progression, find the integral value of x.

Solution: (x + 1), 2 2 and (3x – 2) forms a geometric progression.

Thus, 2 2 is the geometric mean of (x + 1) and (3x – 2)
i.e. 2 2 = (x + 1)(3x – 2)
8 = (x + 1)(3x – 2)
2
8 = 3x + x – 2
2
3x + x – 10 = 0
(3x – 5)(x + 2) = 0
x = 5 or –2
3
Hence, the integral value of x is –2.

Exercise 2.3

th
1. For each of the following geometric series, write down the term indicated in brackets and the n term.
th
(a) 1 + 1 + 2 + … (8 term) (b) 162 + 54 + 18 + … (6 term)
th
2
4
1
th
th
(c) 200 – 50 + 12 + … (5 term) (d) – – 2 – 1 – … (7 term)
2 9 3
2. Find the number of terms in each of the geometric series below, and also the sum of the series.
(a) 1 + 1 + … + 64 (b) 9 – 6 + … + 256
4 2 729
(c) 100 + 50 + … + 25 (d) 2 – 8 + … – 14 2150
16 3 2187
3. Find the sum of each of the following geometric series.
th
th
(a) 100 + 20 + … to 8 term (b) 4 – 2 + … to 10 term
th
th
k
(c) 2 – 6 + … to n term (d) a + a k + 2 + … to n term
4. The terms of a geometric series are positive, with the first term 80. If the sum of the first three terms is
185, find the common ratio of the series.
5. If two numbers, m and n, are such that m, n and 10 form an arithmetic progression, whereas n, m and
10 form a geometric progression, find the values of m and n.

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02 STPM Math T T1.indd 107 3/28/18 4:21 PM