What is the Difference between Arithmetic and Geometric Sequence

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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

Free printable Worksheets

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

Answers

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

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

What is the Difference between Arithmetic and Geometric Sequence