What is the Difference Between Arithmetic Sequence and Geometric Sequence?

The main difference between arithmetic and geometric sequences lies in the way their terms are generated. Here are the key differences between the two:

1. Common Difference vs. Common Ratio: An arithmetic sequence has a constant difference between each consecutive pair of terms, while a geometric sequence has a constant ratio between each pair of consecutive terms.
2. Addition vs. Multiplication: In an arithmetic sequence, terms are generated by adding or subtracting a constant value to the previous term. In a geometric sequence, terms are generated by multiplying or dividing the previous term by a constant value.
3. Increasing or Decreasing: Arithmetic sequences can be increasing or decreasing, depending on the common difference. If the common difference is positive, the sequence is increasing, and if it's negative, the sequence is decreasing. Geometric sequences can also be increasing or decreasing, depending on the common ratio. If the common ratio is greater than 1, the sequence is increasing, and if it's less than 1, the sequence is decreasing.

Examples of arithmetic sequences include:

• 5, 11, 17, 23, 29, 35,… (with a common difference of 6)
• 24, 19, 14, 9, 4, -1, -6,… (with a common difference of -5)

Examples of geometric sequences include:

• 2, 6, 18, 54, 162,… (with a common ratio of 3)
• 15, 8, 4.5, 2.7, 1.5,… (with a common ratio of 0.5)

Comparative Table: Arithmetic Sequence vs Geometric Sequence

Here is a table highlighting the differences between arithmetic and geometric sequences:

An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. In an arithmetic sequence, the next number is calculated by adding or subtracting a constant value to the previous number, whereas, in a geometric sequence, the next number is calculated by multiplying the previous number by a constant value.