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

?, 3, 6.4, 11.5, 18.3, 26.8

Correct Answer: The correct option is 1.3.

To find the missing value in the given sequence, let us analyze the differences between consecutive terms.

The given sequence is:

$?,3,6.4,11.5,18.3,26.8$

Let us compute the differences between each pair of adjacent known terms:

$6.4-3=3.4$

$11.5-6.4=5.1$

$18.3-11.5=6.8$

$26.8-18.3=8.5$

Now, observe the pattern formed by these first-level differences:

$3.4,5.1,6.8,8.5$

Let us check the second-level differences (the difference between successive first-level differences):

$5.1-3.4=1.7$

$6.8-5.1=1.7$

$8.5-6.8=1.7$

The second-level difference is constant and equals 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).

Following this pattern, the first difference prior to 3.4 must be:

$3.4-1.7=1.7$

Let the missing term be $x$. Therefore, the difference between the second term (3) and the first term ($x$) should be 1.7:

$3-x=1.7$

$x=3-1.7=1.3$

Hence, the missing value to fill in the blank space is 1.3.