What is the explicit rule for this geometric sequence?

2, 6, 18, 54, ...

an=3⋅2n-1

an=2⋅3n

an=2⋅3n-1

an=3⋅2n

To find the explicit formula of geometric sequences, you'll need to find a formula for the nth term.

In symbols, the nth term of a geometric sequence is: tn = a·rn-1.

a = first term and r = common ratio

To find the common ratio, divide any term by its preceding term.

Example: 2, 6, 18, 54, 162, ...

a = first term = 2

r = common ratio = 6/3 = 2 (this will be the same anywhere you begin: 162/54 = 3, 54/18 = 3, 18/6 = 3, etc.)

So, the explicit formula is: tn = 2·3n-1

Each explicit formula will have the exponent "n-1".

Your answer would be; tn = 2·3n-1