The sequence given is $14, 7, \frac{7}{2}, \ldots$. To find the 6th term, let's first identify the pattern.

1. The first term is $14$.
2. The second term is $7$ (which is $\frac{14}{2}$).
3. The third term is $\frac{7}{2}$ (which is $\frac{7}{2} = \frac{14}{4}$).

From these, we can see that each term can be expressed as:

• $a_1 = 14$
• $a_2 = \frac{14}{2}$
• $a_3 = \frac{14}{4}$

This suggests that the $n$-th term can be expressed as: $a_n = \frac{14}{2^{n-1}}$

Now, let's calculate the 6th term: $a_6 = \frac{14}{2^{6-1}} = \frac{14}{2^5} = \frac{14}{32} = \frac{7}{16}$

Therefore, the 6th term is $\frac{7}{16}$.

Would you like any further details or explanations? Here are some related questions you might consider:

1. What is the formula for the nth term of this sequence?
2. How would you determine if the sequence is arithmetic or geometric?
3. Can you find the sum of the first six terms?
4. What would be the next term in the sequence after the 6th?
5. How do you derive the common ratio or difference in sequences?

Tip: When working with sequences, try to identify the relationship between terms, as this can often reveal a pattern or formula.