Page 104 - Mathematics_Form_3

Sequences and series

Activity 4.4: Determining the A sequence in which a new term is
amount of money saved for a obtained by multiplying the preceding
certain period of time term by a constant number is known as
a geometric progression. The constant
Individually or in a group, think of any
number is called the common ratio,
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amount of money you would like to
denoted by r.
save. Your plan should be to save a
A geometric series is obtained by adding
certain amount of money every week.
the terms of a geometric progression. For
Follow the following steps: instance, the following are geometric
1. Prepare a table with two columns. series:
The first column should be for (a) 1 + 2 + 4 + 8 + ··· with a common
weeks and the second for amount
of money saved. ratio 2.
1 ___
1 __ 1 __
2. Enter the amount of money you (b) 1 + + + + ··· with a common
3 9 27
want to save in the first week.
1 __
ratio .
3. For the following weeks, double 3
1 __
1 __
1 __
1 ___
the amount you saved the previous (c) + + + + ··· with a
2 4 8 16
week.
1 __
common ratio .
4. Fill in the table the amount saved 2
for 5 weeks. The n term of a geometric
th
5. Study carefully how the amount of progression
money saved varies from the first
to the fifth weeks. If n is the number of terms of a geometric
th
6. Briefly explain the pattern which progression, the n term is denoted by
you think may lead to such an G . It implies that G = r G ,
n n+1 n
increase of the amount of money where r is the common ratio.
saved.
Suppose that 3 is the first term G of a
1
7. Use the pattern obtained from geometric progression whose common
previous steps to formulate a rule ratio r is 2, then the first four terms are
which may allow you to find the
G = 3, G = 3 (2) , G = 3 (2) , and Mathematics for Secondary Schools
2
1
total amount of money saved at any 1 2 3
3
time. G = 3(2) .
4
8. Use the rule you have formulated The n term deduced from the previous
th
in step 7 to determine the amount pattern is given by:
of money that will have been saved
G = 3 ( 2 )
n−1
up to the 10 week. n
th
Therefore, the geometric series in this
9. Share your results with other
students for further discussion. case is:
S = 3 + 6 + 12 + 24 + ··· + 3( 2 ) .
n−1
n
Student\s Book Form Three 97

18/09/2025 09:59:24
MATHEMATIC F3 SB.indd 97 18/09/2025 09:59:24
MATHEMATIC F3 SB.indd 97