Question

Given the arithmetic sequence an = 3 + 2(n − 1), what is the domain for n?

Answer 1

The domain for n is all natural numbers.

Explanation:

An arithmetic sequence is defined as

`a_n=a+(n-1)d` .... (1)

where, a is first term, n is number of term and d is common difference.

The given arithmetic sequence is

`a_n=3+2(n-1)` ... (2)

From (1) and (2), we get

`a=3,d=2`

The first term of the given sequence is 3 and the common difference is 2.

We know that the possible values of n are 1, 2, 3, 4, ....

The sequence is defined form n=1,2,3,4,5,...

The domain of the given arithmetic sequence is all natural numbers.

Therefore the domain for n is all natural numbers.

Answer 2

The domain for n is the natural numbers. i.e. 1, 2, 3, . . .