Question 1114522
it's been a while, so i forgot what a geometric mean is.


fortunately there are references on the web that can help.


here's one.


<a href = "http://www.mathsisfun.com/numbers/geometric-mean.html" target = "_blank">http://www.mathsisfun.com/numbers/geometric-mean.html</a>


based on your description of the problem, you have a series of numbers.


if the first number is x, then:


the second number is 1.1 * x.
the third number is 1.2 * 1.1 * x.
the fourth number is 1.25 * 1.2 * 1.1 * x


this is based on my understanding that each year's increase is based on the salary at the beginning of that year.


the geometric means would therefore be:


the fourth root of (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)


this becomes the fourth foot of (1.1^3 * 1.2^2 * 1.25 * x^4).


this becomes equal to the fourth root of (1.1^3 * 1.2^2 * 1.25) * x.


this becomes equal to the fourth root of (2.3958) * x.


this becomes equal to 1.244121056 * x


if this is true, then (1.244121056 * x) ^ 4 must be equal to (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)


(1.244121056 * x) ^ 4 is equal to 2.3958 * x^4.


(x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x) is equal to 2.3958 * x^4.


this confirms that the geometric mean has been calculated correctly according to the instructions provided by the referenced website.