Question 1189136
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ALL problems like this are invalid.<br>
Given ANY finite sequence of first terms of a sequence, ANY next number makes a valid sequence.  It is mathematically absurd to say that in any problem like this there is only one "right" answer.<br>
Spend as much time (or as little) as you like looking for a logical pattern in the given numbers to predict the next number -- knowing that any answer you come up with might not be "right".<br>
For your first example, there is a logical pattern, assuming you have shown the original sequence incorrectly.  Here is the sequence I see:<br>
3/7, 8/4, 5/9, 10/6, 7/11, 12/8, 9/13<br>
(from one number to the next, add 1 to both numerator and denominator and take the reciprocal)<br>
You left out the term 10/6; and you typed 12/18 instead of 12/8....<br>
For your second example, your answer of 290 makes good mathematical sense.<br>