Which equation represents the formula for the general term, gn , of the geometric sequence 3 , 1 , 1/3 , 1/9 . . .?

Explicit

gn = 3(1/3)^(n-1)

Recursive

gn =1/3gn-1

Step-by-step explanation:

3 , 1 , 1/3 , 1/9 . . .

gn = ar^(n-1)

Where,

a = first term = 3

r = common ratio = 1/3

Check:

g2 = ar^(n-1)

= 3(1/3)^(2-1)

= 3/3^(1)

= 1^1

= 1

The explicit formula is

gn = ar^(n-1)

gn = 3(1/3)^(n-1)

The recursive form for a geometric sequence is gn = rgn-1

recursive form for our sequence gn =1/3gn-1

Where,

gn = 3

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2