I am creating a series by:
1) Multiplying the previous value in the series by a negative constant. For example 100.857 * -0.1 = -10.086, where 100.857 is the previous value and -0.1 is the constant.
2) Calculating the difference between the last value in the series and the value before that. For example, 100.857 - 92.948 = 7.909
3) Summing the last value in the series with the results from steps 1) and 2) to arrive at the next value in the series. For example, 100.857 -10.086 + 7.909 = 98.680.
Repeating this process produces an oscillating series that I think is a sine wave. There is a relationship between the constant and the period of the resulting series. For example, if the constant is -0.1 then the period is approximately 19 iterations. My problem is that I would like to know the formula that relates the constant to the period.
I have attached a spreadsheet that has sample values.