Matchsticks are used to make the letter L, as shown for 1, 2 and 3 letters. Which rule gives the number of matchsticks needed to make n letters?

Imagine you want to describe 'a number doubled, plus three'. Without algebra you would have to make a list: $2\times 1+3=5$; $2\times 2+3=7$; $2\times 5+3=13$; … forever. With a letter — say $x$ for 'the number' — the whole list becomes one short expression: **$2x+3$**. Pick any value of $x$ and you get the right answer. The letter is shorthand for 'whatever number we're talking about'.