A caterpillar is drawn using circles: 1 circle for the head and 3 circles for each body segment. Which rule gives the total number of circles for a caterpillar with n body segments?

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'.