Difference Between Arithmetic Sequence and Linear Function

Mathematicsis not just a branch of study. It is a part of our life. The techniques of maths are applied in our everyday lives. Generally the patterns of the occurrence OS found and then various generalizations are found.

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Some of the real-time samples are also based on the progressions and series. An arithmetic progression is formed by adding the same value to the previous number in order to obtain the next number.

Arithmetic Sequence vs Linear Function

The difference between arithmetic sequence and linear function is that an arithmetic sequence is a sequence of numbers increasing or decreasing with a constant difference whereas a linear function is a polynomial function.

Arithmetic sequence vs Linear function

 

Comparison Table

ParametersLinear AlgebraArithmetic sequence
Branch of MathsIt is used in Calculus and Linear Algebra.It is used in general mathematical calculations which are quite simple.
ValuesHere constant values are obtained.The constant values can not be obtained.
Plotting of GraphOnly a straight line will be obtained.Here the graph can be plotted on both positive and negative sides.
ApplicationTo find the area of space.To count the number of things.
AreaWhen we calculate the area using the plot, we will obtain a constant area.When the area is calculated, the area differs from one to the other.

 

What is Arithmetic Sequence?

An arithmetic sequence is otherwise called as arithmetic progression. An arithmetic sequence is a list of numbers that has a common difference between the numbers.

The constant difference that occurs between the two numbers is called a common difference. It is denoted by ‘d’. This common difference travels along the sequence.

 When  the difference between the consecutive terms is positive the sequence is said to be an increasing sequence. When the difference between the consecutive terms is negative sequence is said to be a decreasing sequence.

  1. If the common difference is positive then the members of the sequence will reach positive infinity
  2. If the common difference is negative then the members of the sequence will reach negative infinity
arithmetic sequence
 

What is Linear Function?

The term Linear Function is now used in two areas of Mathematics. They are Calculus and Linear Algebra. In a Calculus, the linear function will be a straight graph.

In case if calculus or in analytical geometry, the Linear Function is a polynomial whose degree is either one or even less than one. The polynomials that have zero degrees are also included. 

In linear algebra, the linear function is used to obtain the area of a particular space. It is also used to establish a relationship between the two coordinates which will give rise to a third term.


Main Differences Between Arithmetic Sequence and Linear Function

  1. The slope in an arithmetic function can be obtained from the graph. But in a linear function, the slope can be found using the expression
  2. An arithmetic sequence is discrete but a linear function is continuous

References

  1. https://www.sciencedirect.com/science/article/pii/S0096300308008837
  2. https://arxiv.org/pdf/1403.0665
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