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.
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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, ar4 and so on. Where a is the first term and r is the common ratio.
Therefore, the geometric sequence formula is an=arn-1
Geometric sequence example 3, 9, 27, 81…
a=3 r=9/3 n= fifth term
Hence, an=3 X 35-1
The final result is 3 x 81= 243
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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
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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