Subscripts

Consider this equation:

(1)\begin{equation} S_{n+1} = 2S_n + 5 \end{equation}

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 **P _{1}** be the population in 1970,

**P**the population in 1971" and so on.

_{2}We read **P _{1}** 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