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UPSC NDA Math Model Paper 3
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© examsnet.com
Question : 73
Total: 120
What is the geometric mean of the sequence
1
,
2
,
4
,
8
,
_____
,
2
n
?
2
n
∕
2
2
(
n
+
1
)
∕
2
2
(
n
+
1
)
−
1
2
(
n
−
1
)
Validate
Solution:
Given sequence is 1, 2, 4, 8, ______,
2
n
Rewrite the sequence,
2
0
,
2
1
,
2
2
,
.
.
.
.
.
.
.2
n
G
M
=
(
2
0
.
2
1
.
2
2
.
2
3
.
.
.
.
.
.2
n
)
1
n
+
1
⇒
G
M
=
(
2
0
+
1
+
2
+
3
+
.
.
.
.
+
n
)
1
n
+
1
⇒
G
M
=
(
2
n
(
n
+
1
)
2
)
1
n
+
1
⇒
G
M
=
2
n
2
Hence, the geometric mean of the sequence 1, 2, 4, 8, ______,
2
n
is
2
n
2
© examsnet.com
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