On January 1st Komi puts $100 into his bank account. On the first of each month after that he deposits an additional $10.

(a) How much money is in Komi's account at the end of February?

(b) How much money is in Komi's account at the end of March?

(c) How much money is in Komi's account after *n* months?

Answer

Here's the timeline for the money going into Komi's account:

(a) By the end of February Komi has made deposits of $100 (in January) and $10 (in February) so his account contains $110.

(b) By the end of March Komi's account contains $10 more than it did at the end of February, for a total of $120.

(c) At the end of one month (end of January), Komi's account contains $100. At the end of two months (end of February), the account contains

100 + 10.

At the end of three months (end of March), the account contains

100 + 10 × 2.

Generalizing, at the end of *n* months Komi's account contains

100 + 10(*n* – 1) dollars.

And in case you were wondering, no, this problem doesn't have much to do with arithmetic or geometric series. You could look at the amount of money in Komi's account as $100 plus a partial sum of an arithmetic series with *d* = 0, but why bother?