Question

Use a recursive function for the geometric sequence 2, −4, 8, −16, … to represent the 9th term. f(9) = f(1) • (−2)8 f(9) = f(8) • (−2) f(9) = f(1) + −2(8) f(9) = f(8) + −2(8)

Answer 1

Answer:

The answer is $f(9)=f(8).(-2)$

Step-by-step explanation:

Given the geometric sequence 2 , - 4 , 8 , - 16

The first term is 2 and to obtain the second term - 4 we need to multiply the first term by - 2

To obtain  the third term 8 from the second term - 4 we need to multiply - 4 by - 2

We can write this procedure as

$f(n+1)=f(n).(-2)$

This means, to obtain for example the 6th term  [ f(6) ] on the left of the equation we look for the value of n that verifies

$f(n+1)=f(6)$ ⇒ $n+1=6\\n=5$

For the 6th term $n=5$ ⇒

$f(n+1)=f(n).(-2)\\f(5+1)=f(5).(-2)\\f(6)=f(5).(-2)$

With a similar logic, to obtain the 9th term we need $n=8$ ⇒

$f(n+1)=f(n).(-2)\\f(8+1)=f(8).(-2)\\f(9)=f(8).(-2)$

The recursive function that represents the 9th term is

$f(9)=f(8).(-2)$

If we want to know which is the 9th term we can continue the sequence :

2 , - 4 , 8 , - 16 , 32 , - 64 , 128 , - 256 , 512

The 9th term is 512

Answer 2

Answer:

B. f(9) = f(8) • (−2)

Step-by-step explanation: