Question

what is the next fraction in this sequence? simplify your answer. \\(\frac{2}{61}\\), \\(\frac{11}{61}\\), \\(\frac{20}{61}\\), \\(\frac{29}{61}\\), ...

Explanation:

Step1: Analyze denominator pattern

All denominators are 61, so the next denominator is 61.

Step2: Analyze numerator pattern

Calculate the difference between consecutive numerators:
$11 - 2 = 9$
$20 - 11 = 9$
$29 - 20 = 9$
The numerators increase by 9 each time.

Step3: Find next numerator

Add 9 to the last numerator:
$29 + 9 = 38$

Step4: Form the next fraction

Combine the new numerator and denominator.

Answer:

$\frac{38}{61}$