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

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

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?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $140$. -- A Curious Progression