## What is the Difference between Arithmetic and Geometric Sequence

Both arithmetic and geometric sequences follow a pattern, so they are similar. The next number is found in an arithmetic sequence by adding or subtracting the same number. In the same way, the following number in a geometric sequence is found by multiplying or dividing the same number. But the two kinds of sequences are very different from each other.

In this article, we will talk about the big differences between an arithmetic sequence and a geometric sequence.

### Chart of Differences

 Comparative Points Arithmetic Sequence Geometric Sequence Meaning An arithmetic sequence is referred to a list of numbers in which each new term differs from the previous term adding by a fixed amount. A geometric sequence is a series of numbers where each subsequent number is obtained by multiplying the one before it by a fixed amount. Identification Common Difference Common Ratio Advanced by Addition or Subtraction Multiplication or Division Variation of terms Linear Exponential Infinite sequences Divergent Divergent or Convergent

### Exercises for Comparing Arithmetic and Geometric Sequences

For each sequence, state if it is arithmetic, geometric, or neither:

1) $$-5, \ 15, \ -45, \ 135, \ -405, \ ...$$

2) $$7, \ 12, \ 17, \ 22, \ 27, \ ...$$

3) $$56, \ 49, \ 42, \ 35, \ 28, \ ...$$

4) $$78, \ 90, \ 102, \ 114, \ 126, \ ...$$

5) $$48, \ 24, \ 12, \ 6, \ 3, \ ...$$

6) $$192, \ 48, \ 12, \ 3, \ \frac{3}{4} \ , \ ...$$

7) $$-162, \ 54, \ -18, \ 6, \ -2, \ ...$$

8) $$59, \ 46, \ 33, \ 20, \ 7, \ ...$$

9) $$23, \ 39, \ 55, \ 71, \ 87, \ ...$$

10) $$\frac{1}{18} \ , \ \frac{1}{9} \ , \ \frac{2}{9} \ , \ \frac{4}{9} \ , \ \frac{8}{9} \ , \ ...$$

For each sequence, state if it is arithmetic, geometric, or neither:

1) $$-5, \ 15, \ -45, \ 135, \ -405, \ ...$$

$$\color{red}{r \ = \ \frac{15}{-5} \ = \ -3 \ = \ \frac{-45}{15} \ ⇒ \ geometric}$$

2) $$7, \ 12, \ 17, \ 22, \ 27, \ ...$$

$$\color{red}{d \ = \ 12 \ - \ 7 \ = \ 5 \ = \ 17 \ - \ 12 \ ⇒ \ arithmetic}$$

3) $$56, \ 49, \ 42, \ 35, \ 28, \ ...$$

$$\color{red}{d \ = \ 49 \ - \ 56 \ = \ -7 \ = \ 42 \ - \ 49 \ ⇒ \ arithmetic}$$

4) $$78, \ 90, \ 102, \ 114, \ 126, \ ...$$

$$\color{red}{d \ = \ 90 \ - \ 78 \ = \ 12 \ = \ 102 \ - \ 90 \ ⇒ \ arithmetic}$$

5) $$48, \ 24, \ 12, \ 6, \ 3, \ ...$$

$$\color{red}{r \ = \ \frac{24}{48} \ = \ \frac{1}{2} \ = \ \frac{12}{24} \ ⇒ \ geometric}$$

6) $$192, \ 48, \ 12, \ 3, \ \frac{3}{4} \ , \ ...$$

$$\color{red}{r \ = \ \frac{48}{192} \ = \ \frac{1}{4} \ = \ \frac{12}{48} \ ⇒ \ geometric}$$

7) $$-162, \ 54, \ -18, \ 6, \ -2, \ ...$$

$$\color{red}{r \ = \ \frac{54}{-162} \ = \ -\frac{1}{3} \ = \ \frac{-18}{54} \ ⇒ \ geometric}$$

8) $$59, \ 46, \ 33, \ 20, \ 7, \ ...$$

$$\color{red}{d \ = \ 46 \ - \ 59 \ = \ -13 \ = \ 33 \ - \ 46 \ ⇒ \ arithmetic}$$

9) $$23, \ 39, \ 55, \ 71, \ 87, \ ...$$

$$\color{red}{d \ = \ 39 \ - \ 23 \ = \ 16 \ = \ 55 \ - \ 39 \ ⇒ \ arithmetic}$$

10) $$\frac{1}{18} \ , \ \frac{1}{9} \ , \ \frac{2}{9} \ , \ \frac{4}{9} \ , \ \frac{8}{9} \ , \ ...$$

$$\color{red}{r \ = \ \frac{\frac{1}{9}}{\frac{1}{18}} \ = \ 2 \ = \ \frac{\frac{2}{9}}{\frac{1}{9}} \ ⇒ \ geometric}$$

## Comparing Arithmetic and Geometric Sequences Practice Quiz

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