What will be the next number of the series 3, 6, 10.5, 17, 26, ?

To find the next number in the series, we first look at the differences between consecutive terms.

The differences are: $6 - 3 = 3$, $10.5 - 6 = 4.5$, $17 - 10.5 = 6.5$, $26 - 17 = 9$.

Now, we observe the differences: $3, 4.5, 6.5, 9$.

The differences of these differences are: $4.5 - 3 = 1.5$, $6.5 - 4.5 = 2$, $9 - 6.5 = 2.5$.

The second differences are: $1.5, 2, 2.5$.

The next second difference can be assumed to be $3$, leading to a next first difference of $9 + 3 = 12$.

Thus, the next term in the series is $26 + 12 = 38$.

The next number in the series is $38$.