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.