De Mar's Formula Calculator

De Mar's formula, also known as the "arithmetic progression sum formula," is a mathematical equation used to calculate the total sum of an arithmetic sequence over a given number of periods. It's often used in engineering, economics, and finance to calculate cumulative totals when the value of increments changes linearly.

Historical Background

De Mar's formula has been used historically in various fields where incremental values over time need to be summed, such as the analysis of total costs, interest, and savings plans. The formula originates from arithmetic progression theory, a concept in mathematics that dates back to ancient times.

Calculation Formula

The general formula for De Mar’s calculation is:

\[ S = A + B \times \frac{n \times (n + 1)}{2} \]

Where:

• \(S\) = Total sum after \(n\) periods
• \(A\) = Initial value
• \(B\) = Increment value per period
• \(n\) = Number of time periods

Example Calculation

For an initial value \(A = 100\), an increment value \(B = 20\), and \(n = 5\) periods, the calculation would be:

\[ S = 100 + 20 \times \frac{5 \times (5 + 1)}{2} = 100 + 20 \times 15 = 100 + 300 = 400 \]

Thus, the total sum after 5 periods is 400.

Importance and Usage Scenarios

De Mar's formula is important in scenarios involving the accumulation of linear increments over time. For example, in finance, it is used to calculate the total interest earned over time with increasing deposits. In engineering, it can be applied to assess the total cost of projects with regularly increasing expenses.

Common FAQs

1. What is the purpose of De Mar’s formula?

   • De Mar's formula calculates the total sum of a sequence where values increase by a constant increment over time.

2. Where is this formula commonly applied?

   • It is commonly used in finance (for cumulative interest or cost calculation), economics (growth analysis), and project management.

3. What is the difference between this and a geometric progression?

   • De Mar's formula deals with arithmetic progression, where the increment is constant. In contrast, geometric progression involves multiplying by a constant ratio.

De Mar's formula is a powerful tool for understanding cumulative growth and helps in decision-making for financial planning and resource allocation.