Question

Find the radix of the scale in which the numbers denoted by $479,698,907$ are in arithmetical progression.

Answer 1

For $(479{)}_b,(698{)}_b,(907{)}_b$ to be in Arithmetic Progression

$\Rightarrow (479{)}_b+(907{)}_b=2(678{)}_b$

$\Rightarrow (9+7b+4b^2)+(7+9b^2)=2(8+9b+6b^2)$

$\Rightarrow b^2-11b=0$

$\Rightarrow b=11$