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 is \(3 - 1 = 2\), \(5 - 3 = 2\), \(7 - 5 = 2\). So the numerator increases by 2 each time.

Step2: Analyze denominators

The denominator is 13 for all fractions, so it remains 13.

Step3: Find next numerator

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

Step4: Form next fraction

With numerator 9 and denominator 13, the next fraction is \(\frac{9}{13}\).

Answer:

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