Question

In what scale are the radix-fractions $\cdot 16,\cdot 20,\cdot 28$ in geometric progression?

Answer 1

For $(.16{)}_b,(.20{)}_b,(.28{)}_b$ to be in Geometric progression, $(16{)}_b,({20}_b),(28{)}_b$ are also in Geometric progression.

$\Rightarrow (16{)}_b\times (28{)}_b={(20{)}_b}^2$

$\Rightarrow (b+6)(2b+8)=(2b{)}^2$

$\Rightarrow 2b^2-20b-48=0$

$\Rightarrow b=12$