Supriya is writing a recursive function for the arithmetic sequence: -11,-6,-1,4,dots She comes up with: {[t(0)=-11],[t(n)=t(n-1)+5]:} What domain should Supriya use for t 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

Question

Supriya is writing a recursive function for the arithmetic sequence:  -11,-6,-1,4,dots She comes up with:  {[t(0)=-11],[t(n)=t(n-1)+5]:} What domain should Supriya use for  t 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

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Recursive Function: Supriya's recursive function for the arithmetic sequence is given by: $$ t(0) = -11 $$ $$ t(n) = t(n-1) + 5 $$ We need to determine the appropriate domain for $ n $ so that the function generates the given sequence. The sequence starts with $ t(0) $, which means the first term is defined for $ n = 0 $. Since the sequence is arithmetic and each term is found by adding 5 to the previous term, $ n $ should be an integer to maintain the pattern of the sequence. If $ n $ were not an integer, we would not get the terms of the arithmetic sequence, which are separated by a constant difference of 5.Determining the Domain: The sequence is defined starting from $ n = 0 $ and continues with $ n = 1, 2, 3, \ldots $. This means that the domain for $ n $ should include 0 and all positive integers. Therefore, the domain cannot start from $ n = 1 $ because that would exclude the first term of the sequence, $ t(0) = -11 $.Sequence Definition: Since the sequence is arithmetic and each term is obtained by adding a constant to the previous term, the domain of $ n $ must be restricted to integers. If $ n $ were allowed to be any number, we could have non-integer values of $ n $, which would not correspond to the terms of the arithmetic sequence.Restricting the Domain: Based on the previous steps, the correct domain for $ n $ should include 0 and be restricted to integers to maintain the arithmetic sequence. Therefore, the correct answer is: (A) $ n \geq 0 $ where $ n $ is an integer.

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