What are the first five terms of a geometric sequence in which the second term is 6 and the fourth term is 54

2, 6, 18, 54, 162

Step-by-step explanation:

In a geometric sequence, terms that are 2 terms apart (2nd & 4th, for example) have a ratio that is the 2nd power of the common ratio. Since 54/6 = 9 = 3², the common ratio is 3.

The first term will be the 2nd term divided by that ratio; the 5th term will be the 4th term multiplied by that ratio. You can figure the 3rd term any of several ways (and they should all give the same value) : multiply the 2nd term, divide the 3rd term, or find the geometric mean of the 2nd & 4th terms: √ (6·54) = 18.