ANSWER
[tex]a_{6} = 2048[/tex]
EXPLANATION
The general term of a geometric sequence is given by,
[tex] a_{n} = a_{1} ( {r})^{n - 1} [/tex]
The first term of the geometric sequence is 2
[tex]a_{1} =2[/tex]
The common ratio is 4. This means r=5.
The nth term of the sequence is
[tex]a_{n} = 2 ( {4})^{n - 1} [/tex]
The 6th term is
[tex]a_{6} = 2 ( {4})^{6 - 1} [/tex]
[tex]a_{6} = 2 ( {4})^{5} [/tex]
[tex]a_{6} = 2048[/tex]
