Question

David is writing an explicit function for the arithmetic sequence: 10, 13, 16, 19, 10,13,16,19,…10,, 13,, 16, , 19, , He comes up with s(n)=7+3ns(n)=7+3ns, left parenthesis, n, right parenthesis, equals, 7, plus, 3, n. What domain should David use for sss so it generates the sequence?

Answer 1

n ∈ ℕ . . . (Natural numbers)

Explanation:

You want the domain of the relation s(n) = 7+3n so that it defines the sequence 10, 13, 16, ....

Domain

The domain of a function is the set of "input" values for which the function is defined. Here, the function is intended for use with values of n that are Natural numbers:

domain = ℕ

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Additional comment

In general, the domain of any function that defines a sequence will be Natural numbers. That is, values of n will be 1, 2, 3, ....

Occasionally, the sequence represents a relation that is of interest for values of n other than positive integer values. In such a case, the domain may be Whole numbers, or Real numbers.