Consider this equation:

(1)
$$S_{n+1} = 2S_n + 5$$

We are familiar with using letters as variables in phrases such as "let p be the population of a country" or "let B be the birth rate and D be the death rate."

Sometimes we have a series of related values such as the population each year that we could give separate names to (e.g., "let p be the population in 1970, q the population in 1971," etc.) but this gets unwieldy quickly.

An easier approach is to say "Let P1 be the population in 1970, P2 the population in 1971" and so on.

We read P1 as "P sub one."

It is common to think of such numbers as members of a list or set: suppose we have ten years of population data