## Geometric series

A geometric series has first term *a* and common ratio *r*. Choose values for *a*, *r* and the number of terms, *n*, and look at the series displayed.

You will also be given the sum of the first *n* terms, *S*_{n},and the value of .

What values of *r* make *S*_{n} and the value of similar?

**Summary**

Make sure you fully understand how these formulas work:
- each term of a geometric series can be expressed as
*ar*^{n-1}.
- the sum of
*n* terms of a geometric series can be expressed as .
- the sum of an infinite geometric series can be expressed as , when
*|r| < 1*.