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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

Supriya is writing a recursive function for the arithmetic sequence:\newline11,6,1,4, -11,-6,-1,4, \ldots \newlineShe comes up with:\newline{t(0)=11t(n)=t(n1)+5 \left\{\begin{array}{l} t(0)=-11 \\ t(n)=t(n-1)+5 \end{array}\right. \newlineWhat domain should Supriya use for t t so it generates the sequence?\newlineChoose 11 answer:\newline(A) n0 n \geq 0 where n n is an integer\newline(B) n0 n \geq 0 where n n is any number\newline(C) n1 n \geq 1 where n n is an integer\newline(D) n1 n \geq 1 where n n is any number

Full solution

Q. Supriya is writing a recursive function for the arithmetic sequence:\newline11,6,1,4, -11,-6,-1,4, \ldots \newlineShe comes up with:\newline{t(0)=11t(n)=t(n1)+5 \left\{\begin{array}{l} t(0)=-11 \\ t(n)=t(n-1)+5 \end{array}\right. \newlineWhat domain should Supriya use for t t so it generates the sequence?\newlineChoose 11 answer:\newline(A) n0 n \geq 0 where n n is an integer\newline(B) n0 n \geq 0 where n n is any number\newline(C) n1 n \geq 1 where n n is an integer\newline(D) n1 n \geq 1 where n n is any number
  1. Recursive Function: Supriya's recursive function for the arithmetic sequence is given by:\newlinet(0)=11 t(0) = -11 \newlinet(n)=t(n1)+5 t(n) = t(n-1) + 5 \newlineWe need to determine the appropriate domain for n n so that the function generates the given sequence.\newlineThe sequence starts with t(0) t(0) , which means the first term is defined for n=0 n = 0 . Since the sequence is arithmetic and each term is found by adding 55 to the previous term, n n should be an integer to maintain the pattern of the sequence. If n n were not an integer, we would not get the terms of the arithmetic sequence, which are separated by a constant difference of 55.
  2. Determining the Domain: The sequence is defined starting from n=0 n = 0 and continues with n=1,2,3, n = 1, 2, 3, \ldots . This means that the domain for n n should include 00 and all positive integers. Therefore, the domain cannot start from n=1 n = 1 because that would exclude the first term of the sequence, t(0)=11 t(0) = -11 .
  3. Sequence Definition: Since the sequence is arithmetic and each term is obtained by adding a constant to the previous term, the domain of n n must be restricted to integers. If n n were allowed to be any number, we could have non-integer values of n n , which would not correspond to the terms of the arithmetic sequence.
  4. Restricting the Domain: Based on the previous steps, the correct domain for n n should include 00 and be restricted to integers to maintain the arithmetic sequence. Therefore, the correct answer is:\newline(A) n0 n \geq 0 where n n is an integer.

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