1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Sum of n Terms
a 1, a 2, a...
Question
a
1
,
a
2
,
a
3
,.....,
a
n
are in an
A
.
P
.
1
√
a
1
+
√
a
2
+
1
√
a
2
+
√
a
3
+
.
.
.
+
1
√
a
n
−
1
+
√
a
n
=
(
n
−
1
)
√
a
n
+
√
a
1
Open in App
Solution
1
√
a
1
+
√
a
2
+
1
√
a
2
+
√
a
3
+
.
.
.
.
+
1
√
a
n
−
1
+
√
a
n
Let
S
be the Sum and
d
be the common difference
S
=
1
√
a
2
+
√
a
1
+
1
√
a
3
+
√
a
2
+
.
.
.
.
+
1
√
a
n
+
√
a
n
−
1
Rationalising each term, we get
S
=
1
√
a
2
+
√
a
1
+
1
√
a
3
+
√
a
2
+
.
.
.
.
+
1
√
a
n
+
√
a
n
−
1
S
=
√
a
2
−
√
a
1
a
2
−
a
1
+
√
a
3
−
√
a
2
a
3
−
a
2
+
√
a
4
−
√
a
3
a
4
−
a
3
+
.
.
.
+
√
a
n
−
√
a
n
−
1
a
n
−
a
n
−
1
S
=
√
a
2
−
√
a
1
d
+
√
a
3
−
√
a
2
d
+
√
a
4
−
√
a
3
d
+
.
.
.
+
√
a
n
−
√
a
n
−
1
d
S
=
√
a
n
−
√
a
1
d
×
√
a
n
+
√
a
1
√
a
n
+
√
a
1
=
a
n
−
a
1
d
(
√
a
n
+
√
a
1
)
(
1
)
a
n
=
a
1
+
(
n
−
1
)
d
a
n
−
a
1
=
(
n
−
1
)
d
(
2
)
F
r
o
m
(
1
)
a
n
d
(
2
)
S
=
a
n
−
a
1
d
(
√
a
n
+
√
a
1
)
=
(
n
−
1
)
d
d
(
√
a
n
+
√
a
1
)
=
(
n
−
1
)
(
√
a
n
+
√
a
1
)
Suggest Corrections
0
Similar questions
Q.
If
a
r
>
0
;
∀
r
,
n
∈
N
and
a
1
,
a
2
,
a
3
,
.
.
.
.
.
a
2
n
are in A.P, then
a
1
+
a
2
n
√
a
1
+
√
a
2
+
a
2
+
a
2
n
−
1
√
a
2
+
√
a
3
+
a
3
+
a
2
n
−
2
√
a
3
+
√
a
4
+
.
.
.
+
a
n
+
a
n
+
1
√
a
n
+
√
a
n
+
1
=
Q.
If
a
1
,
a
2
,
a
3
,
.
.
.
,
a
n
are in A.P of non-zero terms, Prove that
1
a
1
a
2
+
1
a
2
a
3
+
1
a
3
a
4
+
.
.
.
1
a
n
−
1
a
n
=
n
−
1
a
1
a
n
Q.
If
a
1
,
a
2
,
a
3
,
.
.
.
.
,
a
n
are in A.P. where
a
i
>
0
for all i, show that
1
√
a
1
+
√
a
2
+
1
√
a
2
+
√
a
3
+
.
.
.
.
.
+
1
√
a
n
−
1
+
√
a
n
=
(
n
−
1
)
√
a
1
+
√
a
n
Q.
If
a
1
,
a
2
,
a
3
,
.
.
.
,
a
n
are in A.P. and
a
i
>
0
for all i, then show that
1
a
1
a
2
+
1
a
2
a
3
+
.
.
.
+
1
a
n
−
1
a
n
=
n
−
1
a
1
a
n
.
Q.
If
a
1
,
a
2
,
a
3
,
.
.
.
,
a
n
are in A.P. and
a
i
>
0
for all i, then show that
1
a
1
a
2
+
1
a
2
a
3
+
.
.
.
+
1
a
n
−
1
a
n
=
n
−
1
a
1
a
n
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Arithmetic Progression - Sum of n Terms
MATHEMATICS
Watch in App
Explore more
Sum of n Terms
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app