Analysis and Approaches for IBDP Maths Ebook 1 | Page 70

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 22
1. The first three terms of an infinite geometric sequence are m � 5 , 10, m � 10 , 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
�5m�150 � 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]
2. The first three terms of an infinite geometric sequence are m � 12 , 9, m � 12 , 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 .
2
m � � .
225 0
[4]
(ii) Find the possible values of r .
[6]
(c) (i) If the sequence has a finite sum, state which value of r leads to this sum
and justify your answer.
(ii)
If the sequence does not have a finite sum, find the sum of the first four
terms.
[6]
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