Answer: Option G
[tex]a_6 = -2048[/tex]
Step-by-step explanation:
The geometric series have the following form:
[tex]a_n = a_1 (r) ^ {n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence and r is the common radius.
In this case we know that
[tex]a_1 = -2\\\\r = 4[/tex]
So:
[tex]a_n = -2(4) ^ {n-1}[/tex]
To find the sixth term [tex]a_6[/tex], substitute [tex]n = 6[/tex] in the equation.
[tex]a_6 = -2 (4) ^ {6-1}\\\\a_6 = -2 (4) ^ 5\\\\a_6 = -2048[/tex]
