Answer:
[tex]\bold{a_n=2\cdot(-2)^{n-1}}\\\\or\\\\\bold{a_n=(-1)^{n-1}\cdot2^{n}}[/tex]
Step-by-step explanation:
-4÷2 = -2
8÷(-4) = -2
-16÷8 = -2
So this is a geometric sequence with the first term of 2 and a common ratio of -2
the nth term of a geometric sequence: [tex]a_n=a_1\cdot r^{n-1}[/tex]
Therefore:
[tex]a_n=2\cdot(-2)^{n-1}\\\\a_n=2\cdot(-1\cdot2)^{n-1}=2\cdot(-1)^{n-1}\cdot2^{n-1}=(-1)^{n-1}\cdot2^{n-1+1}\\\\a_n=(-1)^{n-1}\cdot2^{n}[/tex]
