Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 12
1 . The first three terms of an infinite geometric sequence are 10 r , 10 , 10r , where r is the common ratio . The two possible values of r are 1 2 and � 2.
( a ) State which value of r leads to this sum and justify your answer .
( b ) Hence , calculate the sum of the sequence .
[ 2 ]
[ 4 ]
27 2 . The first three terms of an infinite geometric sequence are , 27
2 r r
1 common ratio . The two possible values of r are 3 and � .
3
, 27 , where r is the
( a ) If the sequence has a finite sum , state which value of r leads to this sum and justify your answer .
( b ) If the sequence does not have a finite sum , find the sum of the first four terms .
[ 2 ]
[ 4 ]
3 . The first three terms of an infinite geometric sequence are log2 r
x ,
2 r
log 2
x ,
3 r
log 2
x , where r is the common ratio . The two possible values of the common ratio r are 1 2 and � 2.
( a ) Consider the value of r such that �1� r � 1. Find S � , giving the answer in terms of x .
( b ) Consider the value of r such that r �� 1. Find S
6 when
1 x � .
2
4 . The first three terms of an infinite geometric sequence are u
1
, u2 �m� 2 , u3 � 9 , where
m� . The two possible values of the common ratio r are 4 3 and 1
� . 3
[ 3 ]
[ 4 ]
( a ) Consider the value of r such that �1� r � 1. Find m .
( b ) Hence , calculate the sum of the sequence .
[ 3 ]
[ 4 ]
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