Page 95 - Mathematics_Form_3

Sequences and series

4. The first term of a certain series is (b) Find the value when the fifth
k, the second term is 2k, and the term is divided by the fourth

third term is 3k. Find: term.
(a) the n term. (c) Write down the corresponding
th
(b) the sum of the first ten terms. series.
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(d) Write the expression of the
5. Find the next two terms of the n term of the corresponding
th
following series: series.
(a) 3 + 9 + 27 + 81 + · · · 10. A hall has 10 rows of seats, with

(b) 1 + − 1 + 1 + − 1 + · · · 100 seats in the back row. Each
6. The first term of a certain series is row has 2 fewer seats than the row
a, the second term is ar, and the immediately behind it. How many
third term is a r . Find: seats are there in the hall?
2
(a) the 6 term.
th
(b) the n term. Arithmetic Progression (AP)
th
In everyday life, arithmetic progression
7. If the n term of a certain sequence occurs in scenarios like, employees
th
1
is _______ getting a fixed raise in their salaries every
, find
n(n + 1)
year, and hence the total salary per year
(a) its corresponding series.
forms an arithmetic progression.
(b) the sum of the first three terms.
Engage in Activity 4.3 to familiarize with
8. Consider the series the concept of arithmetic progression.
a + (a d+ ) (a+ + 2 ) (d + a + 3 ) ...d + ...
Activity 4.3: Deducing an
Find the:
Mathematics for Secondary Schools (b) difference between the third 1. Collect an electronic geoboard (or
arithmetic progression
(a) difference between the second
Individually or in a group perform the
and the first term.
following tasks:
and the second term.
matchsticks or toothpicks) from
(c) difference between the fifth and
your subject teacher or you can
the fourth term.
make one from locally available
(d) expression of the general term.
materials such as nails and boards.
9. If a sequence is given as
by arranging rubber bands on a
,
,
2
, a ar ar ar 3 ,... 2. Make a pattern of nested squares
geoboard or arranging matchsticks
(a) Find the value when the second
or toothpicks on the surface of a
term is divided by the first term.
table as shown in Figure 4.3.
88 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 88