Answer:
Explanation:
A typical geometric sequence can be represented as
c
0
a
,
c
0
a
2
,
⋯
,
c
0
a
k
and a typical arithmetic sequence as
c
0
a
,
c
0
a
+
Δ
,
c
0
a
+
2
Δ
,
⋯
,
c
0
a
+
k
Δ
Calling
c
0
a
as the first element for the geometric sequence we have
⎧
⎪
⎨
⎪
⎩
c
0
a
2
=
c
0
a
+
2
Δ
→
First and second of GS are the first and third of a LS
c
0
a
+
3
Δ
=
10
→
The fourth term of the linear sequence is 10
5
c
0
a
+
10
Δ
=
60
→
The sum of its first five term is 60
Solving for
c
0
,
a
,
Δ
we obtain
c
0
=
64
3
,
a
=
3
4
,
Δ
=
−
2
and the first five elements for the arithmetic sequence are
{
16
,
14
,
12
,
10A typical geometric sequence can be represented as
c
0
a
,
c
0
a
2
,
⋯
,
c
0
a
k
and a typical arithmetic sequence as
c
0
a
,
c
0
a
+
Δ
,
c
0
a
+
2
Δ
,
⋯
,
c
0
a
+
k
Δ
Calling
c
0
a
as the first element for the geometric sequence we have
⎧
⎪
⎨
⎪
⎩
c
0
a
2
=
c
0
a
+
2
Δ
→
First and second of GS are the first and third of a LS
c
0
a
+
3
Δ
=
10
→
The fourth term of the linear sequence is 10
5
c
0
a
+
10
Δ
=
60
→
The sum of its first five term is 60
Solving for
c
0
,
a
,
Δ
we obtain
c
0
=
64
3
,
a
=
3
4
,
Δ
=
−
2
and the first five elements for the arithmetic sequence are
{
16
,
14
,
12
,
10