Select the correct value to fill in the blank space of the following sequence:

?, 3, 6.4, 11.5, 18.3, 26.8

The correct option is 1.3.

Let us analyze the given sequence to find the pattern behind the numbers:

?, 3, 6.4, 11.5, 18.3, 26.8

First, let us calculate the differences between consecutive terms starting from the second term:

Difference between 3rd and 2nd term:
6.4 - 3 = 3.4

Difference between 4th and 3rd term:
11.5 - 6.4 = 5.1

Difference between 5th and 4th term:
18.3 - 11.5 = 6.8

Difference between 6th and 5th term:
26.8 - 18.3 = 8.5

Now, let us examine the sequence of first differences obtained:

3.4, 5.1, 6.8, 8.5

Let us find the difference between these consecutive differences (second difference):
5.1 - 3.4 = 1.7
6.8 - 5.1 = 1.7
8.5 - 6.8 = 1.7

We can see that the second difference is constant and equal to 1.7. This indicates an arithmetic progression in the first differences with a common difference of 1.7 (or multiples of 1.7: 1.7 × 2 = 3.4, 1.7 × 3 = 5.1, 1.7 × 4 = 6.8, 1.7 × 5 = 8.5).

To find the missing first term (represented by ?), the difference between the 2nd term (3) and the 1st term (?) must precede 3.4 in this pattern.

Therefore, the first difference between the 2nd and 1st term should be:
3.4 - 1.7 = 1.7

Now, we set up the equation for the first term (?):
3 - ? = 1.7
? = 3 - 1.7
? = 1.3

Thus, the value that fills in the blank space is 1.3.