Question

what is the next fraction in this sequence? simplify your answer.
\\(\frac{1}{13}, \frac{3}{13}, \frac{5}{13}, \frac{7}{13}, ...\\)

Explanation:

Step1: Analyze numerators

The numerators are 1, 3, 5, 7. The difference between consecutive numerators: \(3 - 1 = 2\), \(5 - 3 = 2\), \(7 - 5 = 2\). So the common difference is 2.

Step2: Find next numerator

Next numerator = \(7 + 2 = 9\).

Step3: Analyze denominators

All denominators are 13, so the denominator remains 13.

Step4: Form next fraction

The next fraction is \(\frac{9}{13}\).

Answer:

\(\frac{9}{13}\)