Henry Ernest Dudeney/Puzzles and Curious Problems/140 - A Curious Progression/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $140$

A correspondent sent this:

"An arithmetical progression is $10, 20, 30, 40, 50$, the five terms of which sum is $150$.

Find another progression of five terms, without fractions, which sum to $153$."

The solution given by Dudeney's correspondent, which is as good a solution as any, is:

$153 = 1! + 2! + 3! + 4! + 5!$

where $n!$ denotes the factorial of $n$.

We at $\mathsf{Pr} \infty \mathsf{fWiki}$ came to the same conclusion by clicking on 153, on which this fact is presented.