the first three terms of a geometric sequence are as follows. 2, 6, 18. find the next two terms of this…

Explanation:

Step1: Find the common ratio

The common ratio $r$ of a geometric - sequence is found by dividing a term by its previous term. So, $r=\frac{6}{2}=3$.

Step2: Find the fourth term

The $n$th term of a geometric sequence is given by $a_n=a_1r^{n - 1}$. The fourth term $a_4=a_3\times r$. Since $a_3 = 18$ and $r = 3$, then $a_4=18\times3 = 54$.

Step3: Find the fifth term

The fifth term $a_5=a_4\times r$. Since $a_4 = 54$ and $r = 3$, then $a_5=54\times3=162$.

Answer:

54, 162