Question

If you save two pennies on January 1, four pennies on January 2, six 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 without commas.

Answer 1

.

Answer 2

There's a convenient trick for adding sums like this: On day k, we're saving 2*k pennies, and we are saving for a total of n days. Then we add the number of pennies saved on the kth day to the number added on the (n-k)th day; you'll see that for all values of k, this will be the same.
(For example, we're saving 2 pennies on day 1 and 730 pennies on day 365 for a total of 732 pennies. We're saving 4 on day 2 and 728 on day 364 for a total of 732, etc.)
Then the total number of pennies saved is this sum times half the number of days we're saving for, so 732 * (365/2) = 133590 pennies, or $1335.90

Answer 3

thank you!