Arithmetic Progressions

An arithmetic progression is a progression in which there is a common difference between terms. Subtract any term from the next, and you get the same value.

Example 1

What is the next number in the progression 4, 7, 10, 13, … ?

Since the common difference is 3, the next number is 16.

Example 2

What is the 40th term in the progression 5, 10, 15, 20, … ?

The common difference is 10 – 5 = 5. The 40th term is 36 terms beyond the fourth term, 20.

5 × 36 = 180

equation

5, 10, 15, 20, … , 200

So, the 40th term is 200.