Problem

The given pattern continues. Write down the $n$th term of the sequence $\left\{a_{n}\right\}$ suggested by the pattern.
\[
\frac{1}{14}, \frac{2}{15}, \frac{3}{16}, \frac{4}{17}
\]
\[
\left\{a_{n}\right\}=\{
\]

Answer

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Answer

Final Answer: The nth term of the sequence \(\{a_{n}\}\) is \(\boxed{\frac{n}{n+13}}\)

Steps

Step 1 :Observe the given sequence: \(\frac{1}{14}, \frac{2}{15}, \frac{3}{16}, \frac{4}{17}\)

Step 2 :Notice that the numerator is increasing by 1 each time, and the denominator is also increasing by 1 each time.

Step 3 :This suggests that the nth term of the sequence could be \(\frac{n}{n+13}\).

Step 4 :Final Answer: The nth term of the sequence \(\{a_{n}\}\) is \(\boxed{\frac{n}{n+13}}\)

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