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Sequences and series
5. A geometric progression is a Revision exercise 4
sequence in which a new term
is obtained by multiplying the 1. Find the general term of the
sequence formed by counting the
previous term by a common ratio. natural numbers in three’s starting
The n term of a GP is G = G r , from 1.
, for |r| < 1.READING ONLY
th
n−1
n
1
where G is the first term, r is the 2. The general term of a certain
1
common ratio, and n is the number sequence is ______ . Find the sum
5n − 1
of terms. 2
of the first five terms.
6. A geometric series is the sum of 3. What is the sum of the first n odd
terms of a geometric progression. natural numbers?
7. The formulae for computing the 4. Each year, a coconut tree produces
sum of the first n terms of a GP 3 more coconuts than it did the
are given by, previous year. If it produced 10
coconuts in 1985,
n
G ( r − 1) (a) how many coconuts were
S = _ , for |r| > 1
1
n r − 1 produced in the year 2,000?
or
FOR ONLINE
(b) find the total number of coconuts
G (1 − r ) produced from the year 1985 to
n
S = _
1
n 1 − r year 2000.
8. Compound interest is the interest 5. The starting salary of a worker in a
earned on the principal and certain company is Tshs 2,400,000
the accumulated interest from per annum. If the annual increment
previous period. is Tshs 20,000, what is the total
amount of money earned by the
9. The amount of money A after worker in four years?
n
n years when the interest is th
compounded annually is given 6. Find the n term of the geometric
1 __ 1 __
n sequence 1, , , . . . Mathematics for Secondary Schools
2 4
R
by A = P 1 + ____ .
n ( 100 ) 7. Find the geometric mean and
10. The amount of money A after arithmetic mean of each of the
n
n years when the interest is following sets of numbers:
compounded t times annually is (a) 18 and 72
given by A = P 1+ R nt (b) − 625 and − 2304
n 100t (c) − 4 and − 16
Student\s Book Form Three 109
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MATHEMATIC F3 SB.indd 109 18/09/2025 09:59:29
MATHEMATIC F3 SB.indd 109
