## How to know if a raise is arithmetic or geometric?what is equation for each (to find amount earned on Xth year)?How to find total amount earned during X years?

### To determine whether a raise is arithmetic or geometric, you need to examine the pattern of the raise over time

To determine whether a raise is arithmetic or geometric, you need to examine the pattern of the raise over time.

Arithmetic Raise:

An arithmetic raise is a constant increase or decrease in salary over a period of time. In other words, the raise amount remains the same for every year. To determine the arithmetic raise, you can subtract the initial salary from the final salary and divide it by the number of years. If the difference remains constant for each year, it is an arithmetic raise.

Geometric Raise:

A geometric raise is when the salary changes by a constant factor over a period of time. In other words, there is a fixed percentage increase or decrease in salary each year. To determine the geometric raise, you can calculate the ratio of the final salary to the initial salary. If this ratio remains constant for each year, it is a geometric raise.

To find the amount earned on the Xth year for each type of raise:

Arithmetic Raise:

The equation for an arithmetic raise can be represented as:

Amount earned on Xth year = Initial salary + (Arithmetic raise amount * (X – 1))

Here, “Arithmetic raise amount” refers to the fixed raise value for each year.

Geometric Raise:

The equation for a geometric raise can be represented as:

Amount earned on Xth year = Initial salary * (Geometric raise factor)^(X – 1)

Here, “Geometric raise factor” refers to the constant percentage increase or decrease in salary each year.

To find the total amount earned during X years:

Arithmetic Raise:

The total amount earned during X years can be calculated using the arithmetic series formula:

Total amount earned during X years = (X / 2) * (Initial salary + Final salary)

Here, “X” represents the number of years.

Geometric Raise:

The total amount earned during X years can be found using the geometric series formula:

Total amount earned during X years = Initial salary * ((Geometric raise factor)^(X) – 1) / (Geometric raise factor – 1)

Remember to substitute the appropriate values for the initial salary, final salary, arithmetic/geometric raise amount, and geometric raise factor to obtain accurate results.

It is important to note that these equations assume that the raise amount remains constant over the required time period.

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