The first term of an A.P. is the same as that of a G.P., the common difference of the one and the common ratio of the other are both 4 if the sum of the first three terms of each series are same, find the 14th term of each series.
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Answer:
Let the first term of an A.P and that of G.P be
a
Given that the common difference of one and the common ration of other are both 4.
if the sum of the first three terms of both series are same then
a
+
(
a
+
4
)
+
(
a
+
8
)
=
a
+
4
a
+
16
a
⇒
18
a
=
12
⇒
a
=
2
3
So the fourteenth term of AP is
=
2
3
+
(
14
−
1
)
×
4
=
52
2
3
And the fourteenth term of GP is
=
2
3
×
4
14
−
1
=
=
2
3
×
4
13
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