Page 106 - Mathematics_Form_3

Sequences and series

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Solution 4. If the n term of the geometric
Given G = 75,000,000 Tanzanian series 4 + 8 + 16 + is 1024, find
...
1
shillings, n = 21 years, the value of n.
r = (100 − 25 )% = 75% 5. The value of a machine depreciates
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th
The n term is given by G = G r . each year by 15% of its value at
n−1
n 1 the beginning of that year. If its
Substituting the values into the value when it is new is 2,000,000
formula gives,
Tanzanian shillings, what is its
G = 75000000 (0.75) value after 15 years?
20
21
Tanzanian shillings
6. Find the eighth term of the geometric
= 237,840 Tanzanian progression 2, − 6, 18, − 54, ...
shillings
7. Find the fifth term of the geometric
Therefore, its value after 21 years progression with the first term 100
will be approximately 237,840 and common ratio 0.5.
Tanzanian shillings.
8. A certain school spends 18,500,000
Tanzanian shillings every year
Exercise 4.6 on stationeries. The school
administration decided that each
1. Which of the following are
year the school expenditure
geometric series? Write down their
should be reduced by 10% of the
common ratios.
expenditure of the preceding year.
(a) 3 + 9 + 27 + · · · Find the school expenditure at the

th
1 ___
1 ___
1 __
1 __
(b) + + + + · · · end of the 8 year.
2 6 12 36 9. The second and fifth terms of a
(c) − 1 + 2 − 4 + 8 − · · · geometric progression are 24 and
5,184, respectively. Find;
(d) 2 + 4 − 8 − 16 + · · ·
(a) the common ratio.
2. If the fourth term of a geometric (b) the first term. Mathematics for Secondary Schools
progression is 9 and the sixth term (c) the seventh term.
is 81, find 10. Find the number of terms in each
(a) the common ratio. of the following geometric series:

(b) the first term. (a) 81 + 27 + 9 + · · · + .
1 ___
27
3. The first three terms of a geometric (b) 5 + 10 + 20 + · · · + 5120.
progression are − 4, 1, and − .
1 __
4
Find the fifth term. (c) 0 . 03 + 0 . 06 + 0.12 + · · · + 1 . 92.

Student\s Book Form Three 99

18/09/2025 09:59:24
MATHEMATIC F3 SB.indd 99
MATHEMATIC F3 SB.indd 99 18/09/2025 09:59:24