Let's carefully break down the information given and clarify the sequence based on the terms provided.
1. The first term of the sequence is:
[tex]\[ 1.69 \times 100 = 169.0 \][/tex]
2. The second term of the sequence is:
[tex]\[ \frac{2}{80} = 0.025 \][/tex]
3. The third term of the sequence is:
[tex]\[ 4 - 1 = 3 \][/tex]
With these values, we now have three terms of the sequence:
[tex]\[ 169.0, 0.025, 3, \text{...} \][/tex]
However, there's ambiguity around this sequence's pattern since they don't appear to follow a simple arithmetic or geometric sequence based on the given terms. Without additional context, it's challenging to determine a definite formula for the sequence.
Given the complexity and without further terms or pattern details, let's proceed to see what we can recognize about the sixth term and [tex]\(n\)[/tex]-th term:
### (a) Find the 6th Term
The question asks for the 6th term. Given the provided terms, it is not explicitly clear what the sequence’s pattern would be. Therefore, we retain the 6th term as an undefined value:
[tex]\[ \text{6th term} = \text{None} \][/tex]
### (b) Find the [tex]\(n\)[/tex]th Term
Similarly, identifying a generalized formula for the [tex]\(n\)[/tex]-th term without additional terms or a clear pattern is ambiguous. Thus, the [tex]\(n\)[/tex]-th term remains undefined:
[tex]\[ \text{\(n\)-th term} = \text{None} \][/tex]
To summarize:
- Our first term is [tex]\(169.0\)[/tex].
- Our second term is [tex]\(0.025\)[/tex].
- Our third term is [tex]\(3\)[/tex].
- The sixth term is undetermined given the available information: [tex]\(\text{None}\)[/tex].
- The [tex]\(n\)[/tex]-th term is also undetermined given the available information: [tex]\(\text{None}\)[/tex].
This concludes our detailed analysis and identification of the sequence terms based on the provided information.
