What is the difference between arithmetic and geometric sequence?

A sequence is a set of numbers arranged in a particular order. These set of numbers are known as terms. The main types of sequence are arithmetic and geometric sequence.

**The main difference between arithmetic and geometric sequence is that arithmetic sequence is a sequence where the difference between two consecutive terms is constant while a geometric sequence is a sequence where the ratio between two consecutive terms is constant.**

**Read More: Difference between Area and Perimeter **

## Comparison Table (Arithmetic Sequence vs Geometric Sequence)

Basic Terms |
Arithmetic Sequence |
Geometric Sequence |

Meaning | It is a sequence where the difference between two consecutive terms is a constant | It is a sequence where the ratio between two consecutive terms is a constant |

How to Identify the Sequence | The common difference between successive terms | The common ratio between successive terms |

Mode of Operation | Addition or Subtraction | Multiplication or Division |

Variation of Terms | Linear | Exponential |

Infinite Sequence | Divergent | Either divergent or convergent |

## What Is Arithmetic Sequence?

It is also known as arithmetic progression. It is a sequence where the difference in successive terms is constant.

An arithmetic progression is either added or subtracted. Besides that, it always occurs in a linear form.

Arithmetic sequence example is **a, a+d, a+2d, a+3d, a+4d.** Where **a** is the first term and **d **is a common difference.

Therefore, the arithmetic sequence formula is **a + (n-1) d**

**Question Example**

Identify the first term and calculate the common difference is the sequence. 3, 8, 13, 18, 23 . . .

**a=3 d= second term – first term hence, 8-3 = 5**

## What Is Geometric Sequence?

It is also known as geometric progression. It is a sequence where the ratio between successive terms is constant.

Geometric progression is either multiply or divide. Besides that, a geometric sequence occurs in exponential form.

The common ratio is a fixed and a non-zero number. For instance, **3, 6, 12, 24…** The common ratio here is **2**.

The geometric sequence is expressed as **a, ar, ar², ar³, ar ^{4}** and so on. Where

**a**is the first term and r is the common ratio.

Therefore, the geometric sequence formula is **a _{n}=ar^{n-1 }**

Geometric sequence example 3, 9, 27, 81…

a=3 r=9/3 n= fifth term

Hence, a_{n}=3 X 3^{5-1 }

The final result is 3 x 81= 243

**Read More: Difference between Expression and Equation**

## Main Difference between Arithmetic and Geometric Sequence

- An arithmetic sequence is a list of numbers with successive terms having constant difference whereas geometric sequence is a list of numbers with successive terms having a constant ratio
- An arithmetic sequence has a common difference whereas geometric sequence has a common ratio
- The new term of an arithmetic sequence is either added or subtracted whereas that of a geometric sequence is either multiply or divided
- Variation of members in arithmetic sequence is linear while those of geometric sequence is exponential
- An infinite arithmetic sequence is divergent whereas that of a geometric sequence is either divergent or convergent

## Similarities between Arithmetic and Geometric Sequence

- Both follow a strict pattern
- Both have a constant quantity
- Both tend to confuse students

**Read More: Difference between Length and Height**

## FAQs about Arithmetic and Geometric Sequence

**How Are Arithmetic and Geometric Sequences Similar?**

Both sequence have a constant quantity. This tends to confuse a lot of students while sitting for their exams.

**Are Geometric Sequences Linear?**

No. Geometric sequences are exponential functions such that the n-value increases by a constant value of one and the f (n) value increases by multiples of r.

**Why Is It Called a Geometric Sequence?**

It’s called a geometric sequence because the numbers go from one number to another by diving or multiplying by a similar value.

## Comparison Video

## Conclusion

The above comprehensive information about arithmetic and geometric sequence is quite enough to spearhead easier understanding.

However, these two sequences might appear similar in an examination setup and cause a lot of confusion. Doing more practise will help to resolve the problem.

Calculating questions relating to arithmetic sequence are way simple but those of geometric sequence tend to pose a lot of challenges.

**More Sources and References**

- Sequences and Series. Wind Stream Tutor
- Arithmetic and Geometric Progression. Math Tutor