Two sequences where the second sequence can be found by multiplying each term in the first sequence by the same number are proportional sequences.
- This number is called the coefficient of proportionality.
- The relationship of a term in the first sequence and the term in the same rank in the second sequence is called the proportionality constant or the proportionality relationship.
Example
The sequences s1 = {1, 1, 2, 3, 5, 8, 13, 21, …} and s2 = {2, 2, 4, 6, 10, 16, 26, 42, …} are proportional because we find the second by multiplying each term in the first sequence by 2.
The coefficient of proportionality between these two sequences is 2. The proportionality constant is \(\frac{1}{2}\).