Analysis and Approaches for IBDP Maths Ebook 1 | Page 68

Your Practice Set – Analysis and Approaches for IBDP Mathematics
22
Paper 1 Section B – Condition of
Example
The first three terms of an infinite geometric sequence are 3� m, � 6 , �m
� 2 , where
m� .
(a) (i) Write down an expression for the common ratio, r .
(ii)
Hence, show that m satisfies the equation
(b) (i) Find the two possible values of m .
m
2
� m� 42 � 0.
[4]
(c)
(ii) Find the possible values of r .
The sequence has a finite sum.
[6]
(i)
(ii)
State which value of r leads to this sum and justify your answer.
Calculate the sum of the sequence.
[6]
Solution
(a)
(i)
�6
r � or
3 � m
�m
�2
r �
�6
A1
N1
(b)
(ii)
(i)
�6 �m
� 2
�
3�m
�6
A1
36 � (3 � m)( �m� 2)
A1
36
2
m m 6
2
� � � A1
m � m� 42 � 0
AG N0
2
m � m� 42 � 0
( m� 6)( m�7) � 0
M1
m �� 6 or m � 7
A2 N3
[4]
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