169k views
2 votes
The first and second terms of an exponential sequence (G.P.) are the first and third terms of a linear sequence (A.P.). The fourth term of the linear sequence is 10 and the sum of its first five terms is 60. Find the first four terms of the linear sequence.​

1 Answer

5 votes

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

User Nikit Batale
by
7.4k points