What is the difference between the sum of the 30 term of this sequence?
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Answer:
the difference between the sum of the 30 term of this sequence
Step-by-step explanation:
Given that nth term of the sequence is -
a
n
=
6
n
+
5
So
a
1
=
6
(
1
)
+
5
a
1
=
11
and
a
2
=
6
(
2
)
+
5
a
2
=
17
and
a
3
=
6
(
3
)
+
5
a
3
=
23
and
a
4
=
6
(
4
)
+
5
a
4
=
29
and
a
5
=
6
(
5
)
+
5
a
5
=
35
So the given sequence is-
11
,
17
,
23
,
29
,
35
There is a constant difference between any two terms so the above sequence is an arithmetic sequence.
here
a
=
11
d
=
6
So the sum of
30
terms-
S
30
=
30
2
[
2
(
11
)
+
(
30
−
1
)
6
]
S
30
=
15
[
22
+
174
]
S
30
=
15
[
196
]
S
30
=
2940
So the sum of
30
terms of the given arithmetic sequence is
2940.
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