Final answer:
Upon attempting to find common terms between the two sequences 3n-1 and 7n+2 by setting their formulas equal to each other and solving for n, it turns out there are no integer values of n that satisfy both sequences simultaneously. Therefore, no new sequence can be formed by numbers that appear in both of the original sequences.
Step-by-step explanation:
The student is asking for the formula for the nth term of a new sequence that is formed by the numbers that appear in both the sequences 3n-1 and 7n+2. To find the formula for the nth term, we need to find the values of n for which both the given sequences produce the same numbers.
Let's denote the terms of the first sequence as A(n) and those of the second sequence as B(n), where A(n) = 3n-1 and B(n) = 7n+2. We are looking for the terms that are common in sequences A(n) and B(n).
For these terms to be the same, i.e., A(n) = B(n), we have:
Solving this equation
However, since n must be a positive integer for the sequence terms to exist, we conclude there are no common terms between A(n) and B(n) at integer values of n. Therefore, there is no such sequence with a formula formed by the numbers appearing in both sequences A(n) and B(n).