Question

what is the next fraction in this sequence? simplify your answer. $\frac{5}{7}$, $\frac{34}{49}$, $\frac{33}{49}$, $\frac{32}{49}$, ...

Explanation:

Step1: Unify denominators

Convert $\frac{5}{7}$ to 49 denominator: $\frac{5}{7} = \frac{5 \times 7}{7 \times 7} = \frac{35}{49}$

Step2: Identify sequence pattern

Sequence becomes $\frac{35}{49}, \frac{34}{49}, \frac{33}{49}, \frac{32}{49}, ...$; numerator decreases by 1 each term.

Step3: Find next numerator

Subtract 1 from 32: $32 - 1 = 31$

Step4: Simplify the fraction

$\frac{31}{49}$ is already in simplest form (31 is prime, does not divide 49).

Answer:

$\frac{31}{49}$