Describe the sequence

3.1, 3.14, 3.141, 3.1415, 3.14159, ...

What is the general term *a*_{n}?

Answer

The general term *a*_{n} is the decimal expansion of π to *n* decimal places.

This type of sequence, called a decimal expansion, is probably the most common type of sequence you'll see where the general term is described verbally instead of by a formula. It's easy to understand, but there isn't a simple formula for the general term.

Lucky for us, most sequences you see in calculus classes *will* be described by mathematical formulas because these sequences are easier to work with.

You probably encountered formulas a long time ago. Finding the *n*^{th} term of a sequence is the same as evaluating a mathematical formula. If you don't remember, it's just like riding a bicycle. It'll come back quick.