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Byju's Answer
Standard XII
Mathematics
Sum of n Terms
If sum of fir...
Question
If sum of first
n
terms of an
A
P
(having positive terms) is given by
S
n
=
(
1
+
2
T
n
)
(
1
−
T
n
)
, where
T
n
is the
n
t
h
terms of the series, and
T
2
2
=
√
a
−
√
b
4
(
a
,
b
ϵ
N
)
. Then
(
a
+
b
)
is
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Solution
T
1
=
a
,
T
2
=
a
+
d
S
n
=
(
1
+
2
T
n
)
(
1
−
T
n
)
S
1
=
T
1
=
(
1
+
2
T
1
)
(
1
−
T
1
)
T
1
=
1
+
T
1
−
2
T
2
1
T
1
=
1
√
2
S
2
=
T
2
+
T
1
=
(
1
+
2
T
2
)
(
1
−
T
2
)
T
2
+
T
1
=
1
+
T
2
−
2
T
2
2
2
T
2
2
=
1
−
T
1
T
2
2
=
√
2
−
1
2
√
2
T
2
2
=
√
4
−
√
2
4
=
√
a
−
√
b
4
a
+
b
=
4
+
2
=
6
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0
Similar questions
Q.
In an AP,
t
n
denotes
n
t
h
terms and
S
n
denotes sum of
n
terms. If
t
m
=
1
n
and
t
n
=
1
m
, find
S
m
n
.
Q.
If the
n
t
h
term of the series is
T
n
=
2
n
−
1
, then sum of
n
terms
S
n
will be
Q.
Consider a series whose sum to n-terms is denoted by
S
n
&
n
t
h
term is
t
n
where
S
n
=
n
3
+
2
n
+
1
∀
n
∈
N
, then the value of
(
t
5
−
t
3
)
is equal to
Q.
If
S
n
,
T
n
represents the sum of
n
terms and
n
th
term respectively of the series
1
+
4
+
10
+
20
+
35
+
⋯
, then
n
T
n
+
1
S
n
=
Q.
If
S
n
,
T
n
represents the sum of
n
terms and
n
th
term respectively of the series
1
+
4
+
10
+
20
+
35
+
⋯
, then
n
T
n
+
1
S
n
=
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