Let's have the following sequence of fractions: $\frac{156}{51}, \frac{756}{251}, \frac{3756}{1251}, ? $ .

What fraction replaces the question mark?


1 Answer 1


The next fraction is



the $n$-th fraction is given by $$\frac{30\cdot 5^n+6}{10\cdot 5^n+1}.$$

In other words,

to get the next fraction, keep the last digit of the numerator and denominator, and multiply the number formed by the remaining digits by 5.


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