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

by : $140$

 * A Curious Progression
 * 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 $153$."


 * We noted at once the wily omission of a word in the last sentence,
 * because such an arithmetical progression is not possible.


 * We therefore suggested, by way of jest, this queer solution:
 * a progression of $5$ [then] current silver coins: $3 \oldpence$, $1 \shillings$, $2 \shillings$, $2 \shillings 6 \oldpence$, $4 \shillings$, $5 \shillings$,
 * which sum to $153$ pence.


 * But this is not his own answer, which is quite satisfying -- no algebraic complexities.
 * What is it?