geometric sequences and series:

Question

1. Find the next term of the geometric sequence 2, 10, 50, ...
2. Find the next term of the geometric sequence 9, -3, 1, ....

Answer 1

The key to this type of problem is to try to find the pattern. It will often take some trial and error before coming up with the correct pattern.

In the first series, It seems like each consecutive term is being multiplied by 5. So the series would be,

2, 10, 50, 250, 1250, 6250, etc...

In the second series, we can notice that the terms are going back and forth from positive to negative, and also that each consecutive term is being divided by 3. So the series would be,

9, -3, 1, -1/3, 1/9, -1/27, 1/81, etc...