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Byju's Answer
Standard X
Mathematics
Arithmetic Progression
The sum of fi...
Question
The sum of first
n
terms of a certain series is given as
3
n
2
−
2
n
. Show that the series is an arithmetic series
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Solution
Let sum upto n terms be
S
n
and the
n
t
h
term be
T
n
⇒
S
n
=
3
n
2
−
2
n
and
T
n
+
1
=
S
n
+
1
−
S
n
⇒
T
n
+
1
=
3
(
n
+
1
)
2
−
2
(
n
+
1
)
−
3
n
2
+
2
n
T
n
+
1
=
6
(
n
+
1
)
−
5
Now
T
n
+
1
−
T
n
=
6
=
constant
Hence, this series is an arithmetic series.
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