GOZUNTA
Try it now
All courses Math I · F-IF.3 21 of 59
Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.

Identify the domain of a sequence

Problem
In this sequence, a₁ is the first term, a₂ is the second term, and so on. Which domain matches this indexing?
Your answer
With a free account

Try the session again.

Return to a past session and redo it when you want another look at the same skills.

Create a free account
With paid access

Try the same skill with new numbers.

More variants let you check whether you understand the method instead of remembering one answer.

Compare plans

Hint

Focus on the first index shown. This sequence begins with a₁ and then continues with a₂, a₃, and so on.

The domain of a sequence is the set of allowed term numbers, and those term numbers are discrete inputs rather than every real number.

Solution walkthrough

01

Read the starting index

\[\text{first}~\text{input}:~n~=~1\]

The question says a₁ is the first term, then a₂ is the second term, so the sequence starts with input 1.

02

List the input pattern

\[n~=~1,~2,~3,~4,~...\]

The phrase "and so on" means the sequence continues with term numbers 1, 2, 3, 4, and so forth.

03

Match the domain type

\[\text{positive}~\text{integers}:~n~\ge~1,~\text{where}~n~\text{is}~\text{an}~\text{integer}\]

Counting numbers starting at 1 are positive integers, not nonnegative integers and not a finite set.

04

State the domain

\[\text{domain}:~\text{positive}~\text{integers}~n~\ge~1\]

The domain is the set of possible term numbers for this sequence.

+

Another way

  1. Check the first few inputs: a₁ uses input 1, a₂ uses input 2, and a₃ uses input 3, so the inputs follow the positive integers.

!

Common mistake

A common mistake is to include 0 in the domain just because sequences can sometimes start at a₀. This question starts at a₁, so 0 is not one of the term numbers given.