Page 111 - Mathematics_Form_3

Sequences and series

Exercise 4.8 Engage in Activity 4.5 to learn how to
deduce the general concept of compound
1. Find the geometric mean of each interest as an application of GP.
of the following sets of numbers:
(a) 49 and 81
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(b) − 361 and − 1024 Activity 4.5: Deducing the formula
(c) 4 and 9 for finding compound interest
2. The geometric mean of two numbers
is 12. If one of the numbers is 9, find Individually or in a group, perform the
the other number. tasks:
1. Write down the formula which is
3. The geometric mean of 25 and x is
35. Find the value of x. used to obtain the amount of money
A after one year, that is, the sum of
4. Find the third term, if three numbers 1
are in geometric progression and the principal and simple interest for
their geometric mean is 10, while one year. Factorize the expression
____
the first term is 4. obtained. Remember, I = PRT .
100
5. The geometric mean of two positive 2. Use the amount of money obtained
numbers is 20. If their sum is 50, at the end of the first year as the
find the two numbers. new principal in the second year
6. The geometric mean of two numbers and write the amount of money at
4 and p is 24. Find the value of p. the end of the second year. Factorize
the expression obtained.
7. A rectangular plot of land has sides
of lengths 90 m and 250 m. Use the 3. Use the same procedure to get the
concept of geometric mean to find amount of money at the end of the
third year.
the length of one side of a square 4. Study carefully the final result at
Mathematics for Secondary Schools Compound interest 5. Write a general rule for the increase
having the same area as that of a
rectangular plot.
the end of each year to determine
the pattern in the increase of the
amount of money at the bank. Is the
pattern an arithmetic or a geometric
When money is invested or borrowed
from a bank, the interest is usually
progression? Give reasons.
calculated at the end of the year. The
interest accrued is added to the original
of the amount of money after any
principal at the end of the first year and the
given period of time, say n years.
total amount becomes the new principal
at the beginning of the second year. The 6. Use the rule to determine the
process may continue for a number of amount of money accumulated in
years. This process is called compound the bank after 10 years.
interest.

104 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 104
MATHEMATIC F3 SB.indd 104 18/09/2025 09:59:27