## Workshop: Session 5 — Summary

Before we started talking about sequences, we looked another folding problem involving **medial triangles**.

We started talking about some fun sequences, and we found the next terms for *most of them*. Hopefully no one lost too much sleep over the tricky ones!

We talked a bit about the method of** finite differences** for finding an *n-th term formula* for a given sequences. For example, by looking at the difference of consecutive terms

we see that it takes **two iterations** to get to a **constant difference**. This means that *nth term *of the original sequence is **quadratic**! Naturally, we recognize the original sequence

as **triangle numbers**, and the formula for the *nth *triangle number is well known to be , a quadratic function.

We also looked at some ways to use the method of** finite differences ***backwards , *that is, to find the

**sum**of sequence, i.e. a

**series**. For instance, if we wanted to find the

**sum**of the triangle numbers, we could work

**up**like this

and get the **tetrahedral numbers **(the sequence in **red**), whose formula is well-known to be **cubic**.

In the second half, we looked at several activities that use **Excel** to explore sequences and series. In particular, two of the activities I showed you were taken directly from these videos on Excel and Pascal’s Triangle and Excel and Fibonacci Numbers.

Last, we talked a little about the Purple Comet contest, which is going on now! Get a team together, sign them up, and have fun!