Analysis and Approaches for IBDP Maths Ebook 1 | Page 73

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Exercise 23
1. The first three terms of a geometric sequence are u1 � 800, u2 � 720 and u3 � 648 .
(a) Find the value of r .
(b) Find the value of S
6
.
(c) Find the least value of n such that Sn
� 6400 .
[2]
[2]
[3]
2. The first three terms of a geometric sequence are u1 � 576 , u2 � 768 and u3 � 1024 .
(a) Find the value of r .
(b) Find the value of S
7
.
(c) Find the greatest value of n such that Sn
� 550000 .
[2]
[2]
[3]
6
3. The first three terms of a geometric sequence are u1 �� 324 , u2 �� 540 and u3 �� 900.
(a) Find the value of r .
(b) Find the value of S
10
.
(c) Find the least value of n such that Sn
�� 700000 .
[2]
[2]
[4]
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 .
(b)
Show that
S n
1�n
5 n n
� (5 � 8 ) .
2
(c) Find the greatest value of n such that Sn
�� 100 .
[2]
[2]
[4]
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