Find the sum to infinity of a geometric sequence

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Find the sum to infinity of the geometric sequence −32, −8, −2, …

Remember: Find the common ratio r by dividing a term by the one before it. When −1 < r < 1 the sum to infinity is the first term divided by (1 − r).

The common ratio is −8 ÷ (−32), which is 1/4. It lies between −1 and 1, so the sum to infinity exists.
1 − r = 3/4.
The sum to infinity is −32 ÷ 34, which is −128/3.

Common mistakes

Put the common ratio on top. The first term goes on top.
Multiplied by (1 − r) when the formula divides by it.
Divided the first term by the common ratio, which gives the term before it.