If for an A.P sum of fifth,sixth and seventh term is 51 and t of 10 - t of 9 + t of 8 is 26. Write the sequence of the A.P
Answers
Answer:
Step-by-step explanation:
What is Known?
a
,
l
, and
S
n
What is Unknown?
n
and
l
Reasoning:
Sum of the first
n
terms of an AP is given by
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
or
S
n
=
n
2
[
a
+
l
]
, and
n
t
h
term of an AP is
a
n
=
a
+
(
n
−
1
)
d
Where
a
is the first term,
d
is the common difference and
n
is the number of terms and
l
is the last term.
Steps:
Given,
First term,
a
=
5
Last term,
l
=
45
Sum up to
n
t
h
terms,
S
n
=
400
We know that sum of
n
terms of AP
S
n
=
n
2
(
a
+
l
)
400
=
n
2
(
5
+
45
)
400
=
n
2
×
50
n
=
16
l
=
a
n
=
a
+
(
n
−
1
)
d
45
=
5
+
(
16
−
1
)
d
40
=
15
d
d
=
40
15
d
=
8
3
What is Known?
a
,
l
, and
S
n
What is Unknown?
n
and
l
Reasoning:
Sum of the first
n
terms of an AP is given by
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
or
S
n
=
n
2
[
a
+
l
]
, and
n
t
h
term of an AP is
a
n
=
a
+
(
n
−
1
)
d
Where
a
is the first term,
d
is the common difference and
n
is the number of terms and
l
is the last term.
Steps:
Given,
First term,
a
=
5
Last term,
l
=
45
Sum up to
n
t
h
terms,
S
n
=
400
We know that sum of
n
terms of AP
S
n
=
n
2
(
a
+
l
)
400
=
n
2
(
5
+
45
)
400
=
n
2
×
50
n
=
16
l
=
a
n
=
a
+
(
n
−
1
)
d
45
=
5
+
(
16
−
1
)
d
40
=
15
d
d
=
40
15
d
=
8
3