Answer:
Step-by-step explanation:
The formula for a geometric sequence is
[tex]a_n=a_1*r^{n-1}[/tex] where n is the position number in the sequence, a1 is the first number in the sequence, and r is the common ratio. For us,
n is 14, a1 is 5, and the common ratio (the number we multiply by each number to get to the next one in line) is -2.
[tex]a__{14}=5*(-2)^{14-1}[/tex] and
[tex]a_{14}=5*(-2)^{13}[/tex] and
[tex]a_{14}=5(-8192)[/tex] so
[tex]a_{14}=-40960[/tex]
