Question

*25. what are the next three numbers in this sequence?
\\(\frac{1}{16}\\), \\(\frac{1}{8}\\), \\(\frac{3}{16}\\), \\(\frac{1}{4}\\), \\(\frac{5}{16}\\), \\(\frac{3}{8}\\), \\(\frac{7}{16}\\), _____, ____, ______

Explanation:

Step1: Convert terms to common denominator

Rewrite all fractions with denominator 16:
$\frac{1}{16}, \frac{2}{16}, \frac{3}{16}, \frac{4}{16}, \frac{5}{16}, \frac{6}{16}, \frac{7}{16}$

Step2: Identify sequence pattern

Numerators increase by 1 each term; denominator stays 16.
Next numerators: $7+1=8$, $8+1=9$, $9+1=10$

Step3: Simplify new fractions

$\frac{8}{16}=\frac{1}{2}$, $\frac{9}{16}$ (already simplified), $\frac{10}{16}=\frac{5}{8}$

Answer:

$\frac{1}{2}$, $\frac{9}{16}$, $\frac{5}{8}$