Growth and Decay

Arithmetic growth is modeled by an arithmetic sequence. In an arithmetic sequence each successive term is obtained by adding a fixed quantity to the previous term. For example, an investment that earns simple interest (not compounded) increases by a fixed percentage of the principal (original amount invested) in each period that interest is paid. A one-time investment of $1,000, in an account that pays 5% simple interest per year, will increase by $50 per year. The growth of such an investment, left in place for a 10 year period, is given by the sequence, where the first entry corresponds to the balance at the beginning of the first year, the second entry corresponds to the balance at the beginning of the second year and so on. A sequence that models growth is an increasing sequence, one that models decay is a decreasing sequence. For instance, some banks require depositors to maintain a minimum balance in their checking accounts, or else pay a monthly service charge on the account. If an account, with a required minimum of $500, has $50 in it, and the owner stops using the account without closing it, then the balance will decrease arithmetically each month, by the amount of the monthly service charge, until it reaches zero.