step-by-step instructions for writing an explicit formula for a geometric sequence from a table of values.

Recursive formula for a geometric sequence is

a

n

=

a

n

−

1

×

r

, where

r

is the common ratio.

Explanation:

A geometric series is of the form

a

,

a

r

,

a

r

2

,

a

r

3

,

a

r

4

,

a

r

5

...

...

...

...

...

...

...

...

.

in which first term

a

1

=

a

and other terms are obtained by multiplying by

r

.

Observe that each term is

r

times the previous term. Hence to get

n

t

h

term we multiply

(

n

−

1

)

t

h

term by

r

i.e.

a

n

=

a

n

−

1

×

r

This is called recursive formula for geometric sequence.

There is also explicit formula for

n

t

h

term i.e.

a

n

=

a

×

r

n

−

1

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values