Appreciation is a rate of positive change. So constant appreciation means the rate of change is constant. This implies a linear function, however, the appreciation occurs at certain time intervals, so it is more like an arithmetic sequence.
An example of constant appreciation is simple interest. This is where interest is typically paid on the principal annually. For instance, $1000 is invested in a term deposit at 2% simple interest for 5 years . What is the value of the term deposit at the end of 5 years? 2% of $1000 is $20, so $20 is the constant appreciation. At the end of 5 years, the term deposit would be worth $1100: #$1000+5xx$20#.
Note that most banks pay out using compound interest rather than simple interest.