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)
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Answer:
The answer is
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
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
⇒
For the 6th term ⇒
With a similar logic, to obtain the 9th term we need ⇒
The recursive function that represents the 9th term is
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