Given the arithmetic sequence a_n = 2 - 3(n - 1), what is the domain for n?

Solution:

An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant.

Given a_n = 2 - 3(n - 1)

⇒ a_n = 2 - 3n + 3

⇒ a_n = 5 - 3n

a_n in an AP refers to the nth term of the sequence. The set of values given for n forms its domain.

Give values for n as N = {1, 2, 3, 4, .......}

a₁ = 5-3 = 2

a₂ = 5-6 = -1

a₃ = 5-9 = -4

a₄ = 5-12 = -7

a₅ = 5-15 = -10 and so on.

Thus domain for n is a natural number as n represents the order of the term in the sequence.

Given the arithmetic sequence a_n = 2 - 3(n - 1), what is the domain for n?

Summary:

For the arithmetic sequence a_n = 5 - 3(n - 1), Thus domain for n is a natural number as the order of the term in the sequence.