Question

What is the explicit formula for this sequence?
2,6, 18, 54, 162, ...

Answer 1

`\large\boxed{a_n=2\cdot(3)^(n-1)}`

Explanation:

`2,\ 6,\ 18,\ 54,\ 162,\ ...\\\\2\cdot3=6\\6\cdot3=18\\18\cdot3=54\\54\cdot3=162\\\vdots\\\\\text{It's a geometric series with common ratio}\ r=3,\ \text{and the first term}\ a_1=2.\\\\\text{The explicit formula of a geometric sequence:}\ a_n=a_1r^(n-1).\\\\\text{Substitute:}\\\\a_n=2\cdot(3)^(n-1)`