Formula for a penny every day for a month doubled every day?

Answer 1

If we call the day number "d", the number of pennies "n" and the number you are multiplying by each day "m":

For how many pennies you get on a particular day: n = m^(d-1)

If doubling: subtract 1 from the day number, then raise 2 to the power of that number (using indices) you get the number of pennies.

For how many pennies you would have after a certain number of days: n = 1-(m^d)/(1-m)

If doubling: raise 2 to the power of the day number, then subtract that from 1 (1st part-answer). Subtract 2 from 1 (2nd part-answer), then divide the 1st part-answer by the 2nd part-answer, and you get the cumulative number of pennies.

NB: these formulas can be used for doubling, tripling, quadrupling, halving, quartering, etc. by replacing m with what you would multiply by, and can be used from any starting number. Just multiply your answer with your starting number