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

Verified Answer :

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

Answer:

The domain for n is all natural numbers.

Step-by-step 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.