What is the sum of the first 4 terms of the arithmetic sequence in which the 8th term is 10 and the 14th term is 29.5?
1 answer:
Answer:
Sum of the first 4 terms is
14.50
Explanation:
In an arithmetic sequence, whose first term is
a
and difference between a term and its preceding term is
d
,
the
n
t
h
term is
a
+
(
n
−
1
)
d
and sum of first
n
terms is
n
2
(
2
a
+
(
n
−
1
)
d
)
Hence
6
t
h
term will be
a
+
5
d
=
8
and
10
t
h
term will be
a
+
9
d
=
13
Subtracting first from second,
4
d
=
5
or
d
=
1.25
and
a
=
8
−
5
⋅
1.25
=
8
−
6.25
=
1.75
Hence sum of first four terms is
4
2
⋅
(
2
⋅
1.75
+
3
⋅
1.25
)
=
2
⋅
(
3.5
+
3.75
)
=
2
⋅
7.25
=
14.50
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