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Raymundo is writing an explicit function for the arithmetic sequence:

20,15,10,5,dots
He comes up with

s(n)=20-5n". "
What domain should Raymundo 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

Raymundo is writing an explicit function for the arithmetic sequence:\newline20,15,10,5, 20,15,10,5, \ldots \newlineHe comes up with\newlines(n)=205n s(n)=20-5 n \text {. } \newlineWhat domain should Raymundo use for s s 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. Raymundo is writing an explicit function for the arithmetic sequence:\newline20,15,10,5, 20,15,10,5, \ldots \newlineHe comes up with\newlines(n)=205n s(n)=20-5 n \text {. } \newlineWhat domain should Raymundo use for s s 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. Consider the arithmetic sequence: Raymundo's function for the arithmetic sequence is s(n)=205ns(n) = 20 - 5n. To determine the domain, we need to consider the values of nn that will generate the sequence 20,15,10,5,20, 15, 10, 5, and so on. We start by plugging in values of nn to see if they generate the sequence correctly.
  2. Test n=1 n = 1 : Let's test n=1 n = 1 to see if it generates the first term of the sequence:\newlines(1)=205(1)=205=15 s(1) = 20 - 5(1) = 20 - 5 = 15 \newlineHowever, the first term of the sequence is 20 20 , not 15 15 , so n=1 n = 1 does not generate the first term of the sequence. This means that the domain cannot start with n=1 n = 1 .
  3. Test n=0n = 0: Now let's test n=0n = 0 to see if it generates the first term of the sequence:\newlines(0)=205(0)=200=20s(0) = 20 - 5(0) = 20 - 0 = 20\newlineThis is correct, as the first term of the sequence is 2020. Therefore, the domain should include n=0n = 0.
  4. Determine if n should be an integer: Next, we need to determine if n can be any number or just an integer. Since we are dealing with a sequence, which is a list of numbers in a specific order, n should represent the position of a term in the sequence. Positions in a sequence are always whole numbers, so n should be an integer.
  5. Decide the starting value of n: Finally, we need to decide if n should be greater than or equal to 00 or greater than or equal to 11. Since we have already established that n = 00 generates the first term of the sequence, the domain should start from n = 00.
  6. Determine the domain: Considering the above steps, the domain should be all non-negative integers starting from 00. This means that the correct answer is (A) n0n \geq 0 where nn is an integer, because this domain will generate the sequence 20,15,10,520, 15, 10, 5, and so on.

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