Geometric sequences

Let there be two unknown positive numbers between numbers $12$ and $54$. The first three numbers of these four form $3$ consecutive arithmetic sequence terms, and the last $3$ numbers form three consecutive terms of a geometric sequence. Find the smaller of the two unknown numbers.

Let there be an equilateral triangle with a side length of $16\mathrm{cm}$. Connecting the centres of its sides with line segments we form another equilateral triangle. If we add two more triangles using the same procedure, what is the sum of their areas?

Which of the following numbers cannot be a term of the geometric sequence given by its second term $a_2=360$ and the common ratio $q=\frac{3}{5}$?

Find the sum of the first ten natural powers of the number $2$.