4. If the sum of the first five terms of the sequence is 341 and has a common ratio of 4. find a1
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4. If the sum of the first five terms of the sequence is 341 and has a common ratio of 4. find a1
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Answer:
n
=
5
Explanation:
This is a geometric series with first term
a
1
=
1
and common ratio
r
as
4
1
=
16
4
=
64
16
=
4
The sum of such a series for first
n
terms is given by
S
n
=
a
1
×
r
n
−
1
r
−
1
and as
S
n
=
341
,
a
1
=
1
and
r
=
4
and , we have
1
×
4
n
−
1
4
−
1
=
341
or
4
n
−
1
3
=
341
or
4
n
−
1
=
341
×
3
=
1023
and
4
n
=
1023
+
1
=
1024
=
4
5
Hence,
n
=
5