$x, \ \frac {5x}4, \ \frac 92, \ \ldots$

Given that the above is an arithmetic progression , find the common difference.

The answer is 0.75.

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Relevant wiki: Arithmetic ProgressionsLet $d$ denote the common difference.

Since this is an arithmetic progression, the difference between each consecutive terms are equal, namely,

$\large d = \left( \frac {5x}4 \right) - x = \left( \frac92 \right) - \left( \frac{5x}4\right)$ .

Simplifying the right side, we have

$\large 5x-4x=18-5x$

$\large x=3$

$\large d = \left( \frac {5x}4 \right) - x = \frac { 5(3) }{ 4 } -3$

$\large d=\frac { 3 }{ 4 } =\boxed { 0.75 }$ .