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Question
Mathematics
Number of terms in the sequence 1, 3, 6, 10, 15, …, 5050 is
Q. Number of terms in the sequence
1
,
3
,
6
,
10
,
15
,
…
,
5050
is
1538
203
Sequences and Series
Report Error
A
50
B
75
C
100
D
125
Solution:
Let
S
=
1
+
3
+
6
+
10
+
15
+
,
…
,
+
t
n
(
1
)
then
S
=
1
+
3
+
6
+
10
+
,
…
,
+
t
n
−
1
+
t
n
(
2
)
(
1
)
−
(
2
)
⇒
0
=
(
1
+
2
+
3
+
4
+
…
to
n
terms
)
−
t
n
⇒
t
n
=
2
n
(
n
+
1
)
Given,
5050
=
2
n
(
n
+
1
)
⇒
n
2
+
n
−
10100
=
0
⇒
n
=
2
−
1
±
1
+
40400
=
2
−
1
±
40401
=
2
−
1
±
201
=
−
101
,
100
∴
n
=
100.
(
∵
n
is a positive integer
)