Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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