Page 117 - Mathematics_Form_3

Sequences and series

8. The second, fourth, and eighth 15. The amount of money A
n
terms of an arithmetic progression accumulated from the principal
form the first three terms of a P invested at R% interest rate
geometric progression, while the compounded annually for n
sum of the third and fifth terms years is given by the formula
FOR ONLINE READING ONLY
n
of the geometric progression is A = P 1 + ____ . Find A if
R
)
(
100
n
n
20. Find the first four terms of the P = Tsh 1,260,000 , R = 4 % , and
geometric progression.
n = 5 years.
9. Find the difference between 16. The 2 , 4 , and 9 terms of an
th
nd
th
the sum of the first ten terms of
the arithmetic progression and arithmetic progression form a
geometric progression. Find the
geometric progression whose first
common ratio of the geometric
two terms are − 2, 4, ...
progression.
10. Find the sum of the first n terms 17. A hardware dealer stacks pipes in
of the geometric progression his store so that the bottom row
x, − x , x , . . . has 29 pipes, the second row has
2
3
11. A geometric progression has 28 pipes, and subsequently each
G = 2 and G = 4. Find the row above has one pipe less than
2
1
product of the first 100 terms. one below it. There are 15 rows
in total. How many pipes does
12. Find the amount of money at the he have?
end of the second and third years
18. Find the sum of all two-digit
if Tsh 200,000 is invested at 5%
positive integers that are divisible
interest compounded annually.
by 7. n fn + gn , where
Mathematics for Secondary Schools 14. A company borrows Tshs 2,000,000 20. Find the n term of the sequence
13. In how many years would one’s
19. The sum of a certain series is
investment double, if 5,000,000
given as S =
2

Tanzanian shillings is invested at
, fg ∈
. Show that the series is
5.5% interest compounded semi-
an AP, and write the general term.
annually?
th
given by log 96, log 24, and
2
2
from a bank at 7% interest rate
log 6.
2
compounded annually, and repays
500,000 Tanzanian shillings at the
sequence (a −
4), (a +
1), ,b 5a
end of each year. How much does
form an AP, and the last three
the company still owe the bank at 21. The first three terms of the
the end of two years? terms form a GP. Find the values
of a and .b
110 Student\s Book Form Three

MATHEMATIC F3 SB.indd 110 18/09/2025 09:59:29
18/09/2025 09:59:29
MATHEMATIC F3 SB.indd 110