Geometric sequences

Let there be four numbers, such that the first three numbers form consecutive arithmetic sequence terms with a difference of $d=-6$, and the last three numbers form consecutive terms of a geometric sequence with the common ratio $q=\frac{2}{3}$. Find the fourth number.

Let there be three numbers that are $3$ consecutive arithmetic sequence terms. Their sum is $9$. If the first number is divided by $-3$, we get $3$ consecutive terms of a geometric sequence. Find the largest number of the given three.

Let there be a row of five yellow cubes lying side by side. The first cube has an edge length of $100\mathrm{cm}$ and each next cube has an edge length by $10\mathrm{cm}$ shorter than the previous one. Let there be a second row of five blue cubes lying side by side. The first blue cube has an edge length of $100\mathrm{cm}$ and each next cube has an edge length by $10\mathrm{\%}$ smaller than the previous one. What is the difference between the length of these two rows?

The lengths of a cuboid edges form $3$ consecutive terms of a geometric sequence. The volume of the cuboid is $140608{\mathrm{cm}}^3$, the sum of its shortest and its longest edge is $221\mathrm{cm}$. Find the length of its shortest edge.