Question

create the explicit formula for the sequence 2 8 14

Answer 1

Step-by-step explanation:

Explanation:

This looks like an arithmetic sequence, so we start by finding the common difference

d

.

d

=

a

n

–

a

n

−

1

Your sequence is

[

−

4

,

2

,

8

,

14

,

…

]

.

For

a

2

,

d

=

a

2

−

a

1

=

2

–

(

−

4

)

=

2

+

4

=

6

For

a

3

,

d

=

a

3

−

a

2

=

8

−

2

=

6

For

a

4

,

d

=

a

4

−

a

3

=

14

−

8

=

6

So

d

=

6

.

The general formula for an arithmetic sequence is

a

n

=

a

1

+

(

n

−

1

)

d

.

So, for your sequence, the general formula is

a

n

=

−

4

+

6

(

n

−

1

)

=

−

4

+

6

n

−

6

.

a

n

=

6

n

−

10