What will be the next number of the series

3, 6,10.5,17,26,?

The correct option is 37.5.

To find the next number in the given series, we first analyze the differences between consecutive terms:

First term to second term difference:
$$6-3=3$$

Second term to third term difference:
$$10.5-6=4.5$$

Third term to fourth term difference:
$$17-10.5=6.5$$

Fourth term to fifth term difference:
$$26-17=9$$

Now, we look at the progression of these differences: 3, 4.5, 6.5, and 9. Let's find the differences between these consecutive differences (the second-order differences):

First increment:
$$4.5-3=1.5$$

Second increment:
$$6.5-4.5=2$$

Third increment:
$$9-6.5=2.5$$

Following this pattern of differences, the next term is obtained by adding the last difference increment (2.5) to the previous difference (9) to get the next term's difference:

Next difference in the sequence:
$$9+2.5=11.5$$

Adding this difference to the last term in the series (26) gives the next number of the series:

Next number:
$$26+11.5=37.5$$