Consider the following geometric sequence.

2,6,18,54 ...

The recursive formula for the sequence is?

A: an=3*an-1

B: an=2*3^n-1

The explicit formula for the sequence is?

A: an=2*3^n-1

B: an=3*an-1

2,6,18,54 ...

the sequence above has a common ratio of:

6/2=3

hence it is a geometric sequence.

a] The recursive formula of the sequence will be:

common ratio=3

first term a1=2

an=3a_ (n-1)

Answer: A

b] The explicit formula is given by:

an=ar^ (n-1)

where

a=first term

r=common ratio

thus the formula will be:

an=2*3 ⁽ⁿ⁻¹⁾

Answer: A