The given sequence is 2, 6, 18, 54, ...
Notice that this is a geometric sequence because here we have equal common ratio.
So, common ratio : [tex] r = \frac{a_{2}}{a_{1}} [/tex]
=[tex] \frac{6}{2} [/tex]
= 3
The formula for general term of a geometric sequence is,
[tex] a_{n} =a_{1}* r^{n-1} [/tex]
Where, first term: a_{1} =2
Next step is to plug in these values in the above equation to get the formula for the given sequence.
[tex] a_{n} =2* 3^{n-1} [/tex]
Hence, the correct choice is A.
