Raymundo is writing an explicit function for the arithmetic sequence:20,15,10,5,…He comes up withs(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
Q. Raymundo is writing an explicit function for the arithmetic sequence:20,15,10,5,…He comes up withs(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
Consider the arithmetic sequence: Raymundo's function for the arithmetic sequence is s(n)=20−5n. To determine the domain, we need to consider the values of n that will generate the sequence 20,15,10,5, and so on. We start by plugging in values of n to see if they generate the sequence correctly.
Test n=1: Let's test n=1 to see if it generates the first term of the sequence:s(1)=20−5(1)=20−5=15However, the first term of the sequence is 20, not 15, so n=1 does not generate the first term of the sequence. This means that the domain cannot start with n=1.
Test n=0: Now let's test n=0 to see if it generates the first term of the sequence:s(0)=20−5(0)=20−0=20This is correct, as the first term of the sequence is 20. Therefore, the domain should include n=0.
Determine if should be an integer: Next, we need to determine if 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, should represent the position of a term in the sequence. Positions in a sequence are always whole numbers, so should be an integer.
Decide the starting value of : Finally, we need to decide if should be greater than or equal to or greater than or equal to 111. Since we have already established that n = 000 generates the first term of the sequence, the domain should start from n = 000.
Determine the domain: Considering the above steps, the domain should be all non-negative integers starting from 000. This means that the correct answer is (A) n≥0n \geq 0n≥0 where nnn is an integer, because this domain will generate the sequence 20,15,10,520, 15, 10, 520,15,10,5, and so on.
More problems from Evaluate recursive formulas for sequences