Analysis and Approaches for IBDP Maths Ebook 1 | Page 67

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Exercise 21
1. The first three terms of an infinite geometric sequence are 1024, 256 and 64.
(a)
Write down the value of r , the common ratio of the geometric sequence.
(b) Find u
8
.
(c)
Find the sum to infinity of this sequence.
[1]
[2]
[2]
2. The first three terms of an infinite geometric sequence are
x � 0 .
48
ln x ,
24
ln x and
12
ln x , where
(a)
Find the common ratio of the geometric sequence.
(b) Find u
6
.
(c)
Find the sum to infinity of this sequence.
3. The first three terms of an infinite geometric sequence are
12x
e ,
8x
e and
4x
e .
[3]
[2]
[2]
6
(a)
Find the common ratio of the geometric sequence.
(b) Find u
7
.
(c)
Find x if the sum to infinity of this sequence is
e
96
[2]
[2]
24
e � 1
. [3]
4. The first three terms of an infinite geometric sequence are
10
3 x ,
9
3 x and
8
3 x .
(a)
(b)
(c)
Find the common ratio of the geometric sequence.
Find a general expression for u
n
.
Find the sum to infinity if the common ratio is 1 , giving the answer in the form
3
[2]
[3]
a� 3 b .
[3]
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