Let's analyze the given sequence [tex]\((-3, 5, -7, 9, -11, \ldots)\)[/tex] and verify each of the given statements step by step.
1. The sequence has 5 terms.
To determine if the sequence has 5 terms, we simply count the terms in the provided sequence.
- The terms provided are [tex]\(-3, 5, -7, 9, -11\)[/tex].
There are indeed 5 terms in the sequence. Hence, the statement is True.
2. The 4th term of the sequence is 9.
To verify this, we need to identify the term at position 4 in the sequence.
- The sequence is given as [tex]\((-3, 5, -7, 9, -11)\)[/tex].
- The 4th term in this list is [tex]\(9\)[/tex].
Therefore, the statement is True.
3. [tex]\( f(5) = 2 \)[/tex]
We need to check the value of the sequence at position 5. In the list:
- The term at the 5th position is [tex]\(-11\)[/tex].
Therefore, [tex]\( f(5) = -11 \)[/tex], not [tex]\(2\)[/tex]. Hence, the statement is False.
4. The domain of the sequence is all natural numbers.
- By definition, the domain of a sequence typically includes all natural numbers (i.e., positive integers [tex]\(1, 2, 3, \ldots\)[/tex]) because these represent the positions of the terms in the sequence.
Therefore, the statement is True.
5. [tex]\( (4, 9) \)[/tex] lies on the graph of the sequence.
To determine if the point [tex]\((4, 9)\)[/tex] lies on the graph, we check if the term at position 4 in the sequence is 9.
- As established earlier, the 4th term in the sequence is [tex]\(9\)[/tex].
Thus, the point [tex]\( (4, 9) \)[/tex] is indeed on the graph of the sequence. Hence, the statement is True.
Summarizing the results:
- 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
