PLEASE HELP ME ASAP PLEASE FAST AS YOU CAN

Question

Use a recursive function for the geometric sequence 2, −4, 8, −16, … to represent the 9th term.

A.f(9) = f(1) • (−2)⁸ 

B.f(9) = f(8) • (−2) 

C.f(9) = f(1) + −2(8) 

D.f(9) = f(8) + −2(8)

Answer 1

For a geometric series, the formula for the nth term is

A(n) = a(r)^n-1

a is the first term in the series

r is the common ratio

n is the term you are trying to find.

For this example

a=f(1)

r = -2 (This is because you multiply each term by -2 to get the next term)

n=9 since you are looking for the 9th term

Plugging all this into the formula you get

f(9) = f(1)(-2)^9-1 Simplifies to

f(9) = f(1)(-2)⁸ which is A