What is the explicit rule for this geometric sequence?2, 6, 18, 54, …an=3⋅2n−1an=2⋅3nan=2⋅3n−1an=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 ratioTo find the common ratio, divide any term by its preceding term.Example:  2, 6, 18, 54, 162, ...a = first term = 2r = 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-1Each explicit formula will have the exponent "n-1".Your answer would be; tn  =  2·3n-1