Which term 128 is of the progression 1.2.
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MATHS
Which term of the following sequences :
(a) 2,2
2
,4,...is128?
(b)
3
,3,3
3
,... is 729?
(c)
3
1
,
9
1
,
27
1
,... is
19683
1
?
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ANSWER
(a) The given sequence is, 2,2
2
,4,...
Clearly given sequence is in G.P
With a=2 and r=
2
2
2
=
2
Let the n
th
term of the given sequence be 128.
a
n
=ar
n−1
⇒(2)(
2
)
n−1
=128
⇒(2)(2)
2
n−1
=(2)
7
⇒(2)
2
n−1
+1
=(2)
7
⇒
2
n−1
=6⇒n−1=12⇒n=13
Thus, the 13
th
term of the given sequence is 128.
(b) The given sequence is
3
,3,3
3
Clearly this sequence is in G.P
with, a=
3
and r=
3
3
=
3
Let the n
th
term of the given sequence be 729.
a
n
=ar
n−1
⇒ar
n−1
=729
⇒(
3
)(
3
)
n−1
=729
⇒(3)
2
1
(3)
2
n−1
=(3)
6
∴
2
1
+
2
n−1
=6
⇒
2
1+n−1
=6
⇒n=12
Thus, the 12
th
term of the given sequence is 729.
(c) The given sequence is,
3
1
,
9
1
,
27
1
,...
Clearly this sequence is in G.P
With a=
3
1
and r=
9
1
÷
3
1
=
3
1
Let the n
th
term of the given sequence be
19683
1
a
n
=ar
n−1
⇒ar
n−1
=
19683
1
⇒(
3
1
)(
3
1
)
n−1
=
19683
1
⇒(
3
1
)
n
=(
3
1
)
9
⇒n=9
Thus, the 9
th
term of the given sequence is
19683
1