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![Abraham is writing a recursive function for the geometric sequence:
24,12,6,3,dots
He comes up with:
{[s(1)=24],[s(n)=s(n-1)*(1)/(2)]:}
What domain should Abraham use for
s so it generates the sequence?
Choose 1 answer:
(A)
n >= 0 where
n is an integer
(B)
n >= 0 where
n is any number
(C)
n >= 1 where
n is an integer
(D)
n >= 1 where
n is any number](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/Algebra-1/Sequences/General%20sequences/Q-41.png)
Abraham is writing a recursive function for the geometric sequence:He comes up with:What domain should Abraham use for so it generates the sequence?Choose answer:(A) where is an integer(B) where is any number(C) where is an integer(D) where is any number
Full solution
Q. Abraham is writing a recursive function for the geometric sequence:He comes up with:What domain should Abraham use for so it generates the sequence?Choose answer:(A) where is an integer(B) where is any number(C) where is an integer(D) where is any number
- Sequence Definition: Abraham's sequence starts with and each subsequent term is half of the previous term. This is a geometric sequence with a common ratio of . The first term, , is given as . To generate the sequence, we need to determine the correct domain for the function that will produce the terms of the sequence.
- Domain Considerations: The domain of a function is the set of all possible input values (, in this case) for which the function is defined. Since we are dealing with a sequence, the input values should be integers because sequences are defined for integer indices. Therefore, we can eliminate options (B) and (D) because they allow to be any number, not just integers.
- Starting Point of Sequence: Next, we need to consider whether the sequence should start from or . Since the first term is given by , the sequence starts at . This means that the domain should include starting from , not . Therefore, option (A) is also not suitable because it includes .
- Correct Domain for the Function: The correct domain for the function is the set of all integers starting from . This is because the sequence starts with the first term , and each term is defined for positive integer values of . Therefore, the correct answer is where is an integer.
