Let's analyze each statement based on the given sequence [tex]\(-3, 5, -7, 9, -11, \ldots\)[/tex]:
1. The sequence has 5 terms.
- To determine the number of terms in the sequence, we simply count them: [tex]\(-3, 5, -7, 9, -11\)[/tex].
- There are 5 terms in total.
- Therefore, this statement is True.
2. The 4th term of the sequence is 9.
- To identify the 4th term in the sequence, we look at the position of each term:
- 1st term: [tex]\(-3\)[/tex]
- 2nd term: [tex]\(5\)[/tex]
- 3rd term: [tex]\(-7\)[/tex]
- 4th term: [tex]\(9\)[/tex]
- Therefore, this statement is True.
3. [tex]\(f(5) = 2\)[/tex]
- The 5th term of the sequence is [tex]\(-11\)[/tex], so [tex]\(f(5)\)[/tex] is equal to [tex]\(-11\)[/tex].
- Since [tex]\(f(5) \neq 2\)[/tex], this statement is False.
4. The domain of the sequence is all natural numbers.
- In a typical sequence, the domain refers to the set of positions that index the terms of the sequence. These positions are usually counted using natural numbers: [tex]\(1, 2, 3, \ldots\)[/tex].
- Therefore, it is correct to say that the domain of the sequence is all natural numbers.
- This statement is True.
5. [tex]\((4, 9)\)[/tex] lies on the graph of the sequence.
- To determine if [tex]\((4, 9)\)[/tex] lies on the graph of the sequence, we check if the value of the sequence at position [tex]\(4\)[/tex] (i.e., the 4th term) is [tex]\(9\)[/tex].
- The 4th term in the given sequence is [tex]\(9\)[/tex].
- Therefore, [tex]\((4, 9)\)[/tex] indeed lies on the graph of the sequence.
- This statement is True.
In summary:
- The sequence has 5 terms. (True)
- The 4th term of the sequence is 9. (True)
- [tex]\(f(5) = 2\)[/tex]. (False)
- The domain of the sequence is all natural numbers. (True)
- [tex]\((4, 9)\)[/tex] lies on the graph of the sequence. (True)
