Given the following incomplete number sequence:

15, 39, $\frac{1}{8}$, $\frac{1}{49}$, 100, 11, __, __

What are the two missing values?

  • 5
    $\begingroup$ Welcome to Puzzling. A couple of points, 1) It appears as if your question got cut off... I've attempted to fix it based on the title, but you should review. 2) You may want to have a look at this meta post which includes tips on writing number sequence puzzles. $\endgroup$
    – Alconja
    Oct 8, 2017 at 23:05
  • 2
    $\begingroup$ $15+39+8+49 = 100+11$, seems to have the format $\frac{15}{1} , \frac{39}{1} , \frac{1}{8} , \frac{1}{49}, \frac{100}{1}, \frac{11}{1},\frac{1}{?}, \frac{1}{?}$. So, the last two question marks will sum to $168$? Also $(15-8)^2 = 49, (49-39)^2 = 100$. $\endgroup$ Oct 9, 2017 at 20:36

1 Answer 1


I think the answer would be:

$\frac{1}{8464}, \frac{1}{1444}$


as @Carl Löndahl points out in the comments, the sequence appears to have the format $\frac{15}{1}, \frac{39}{1}, \frac{1}{8}, \frac{1}{49}, \frac{100}{1}, \frac{11}{1}$. Therefore the next numbers should be $\frac{1}{?}, \frac{1}{?}$

The fourth value is the squared difference between the numerator of the first number and the denominator of the third number: $(15-8)^2 = 49$. This also holds for the fifth number: $(39-49)^2 = 100$
Thus the sixth number should be: $(8-100)^2 = 8464$ and the seventh number should be $(49-11)^2 = 1444$.

Combing the the found numbers with the format of the sequence and the total sequence will become:
$\frac{15}{1}, \frac{39}{1}, \frac{1}{8}, \frac{1}{49}, \frac{100}{1}, \frac{11}{1}, \frac{1}{8464}, \frac{1}{1444}$


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