Many people in sales, marketing, or general management roles are asked to provide forecasts. Not everyone has sophisticated analytical software tools, or feels comfortable tackling the math. Here is a real-life example of how you can use a straight line (arithmetic progression) to create a forecast with ease and confidence. Assume management has said the company will grow at an 8% rate this year. Last year your quota was $5M dollars, so you can calculate that this year it will be $5.4M. But how do you calculate the individual months so that they add up to $5.4M, and have a growth rate of 8%? An arithmetic progression provides the answer.

EXAMPLE 1:
Given: S_n = $5,400,000,  n = 12,  y = 8%

Find: a₁-a₁₂.

Table 1

Table 1 shows the calculated values used in Graph 1, which plots the results for each month a₁-a₁₂. A spreadsheet can facilitate some quick what if's and can be built using the following information. The equation for an arithmetic progression is, S_n=n/2[2a₁+(n-1)d]. Where: S_n is the sum of n terms, n is the number of terms, a₁ is the first term, a_n is the nth term, d is the common difference and y is the growth rate. Other useful rearrangements of the original equation are: a₁ = 2S_n/[n(2+y)], d = a₁y/(n-1) and a_n = a₁+(n-1)d.