Question

If you save one penny on January 1, two pennies on January 2, three pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal.

Answer 1

The given condition is an arithmetic sequence with the first term (a1) is 1 penny and the common difference (d) is 1 penny. A year that is not a leap year has 365 days (n). The arithmetic series (S) is calculated through formula,
 
                               S = (n/2) (2a1 + (n - 1) x d)

Substituting the known values,
 
                               S = (365/2) (2 x 1 + (365 - 1) x 1)
 
                               S = 66795 pennies

A dollar is 100 pennies. Therefore, at the end of the year, the total savings is $667.95.