Apps. and Interpretation for IBDP Maths Ebook 1 | Page 74

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 20
1. The first three terms of a geometric sequence are 1024, 256 and 64.
(a) Write down the value of r , the common ratio of the geometric sequence.
[1]
(b) Find u
8
.
[2]
(c) Find the sum of the first twelve terms of this sequence, giving the answer correct
to the nearest integer.
[3]
2. The first three terms of a geometric sequence are u1 � 576 , u2 � 768 and u3 � 1024 .
(a) Write down the value of r .
(b)
Find the value of
7
�
n�1
u
n
, giving the answer correct to the nearest integer.
(c) Find the value of n such that 243u n
� 1048576 .
[1]
[3]
[3]
3. The first three terms of a geometric sequence are u1 � 1.024 , u2 � 1.28 and u3 � 1.6 .
(a) Find the value of r .
(b) Find the least value of n such that un
� 5 .
(c)
Find the value of
10
� un
.
n�1
[2]
[3]
[2]
4. The first three terms of a geometric sequence are u1 � 1.5 , u2 � 2.4 and u3 � 3.84 .
(a) Find the value of r .
[2]
(b) Find the value of the eighth term of the sequence, giving the answer correct to two
decimal places.
[2]
(c) Find the greatest value of n such that Sn
� 100 .
[3]
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