Some formulas of Arithmetic progression/series

[burgess]

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Example: 2,4,6,8,10…..

Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series.
Example: 2+4+6+8+10…..

nth term in the finite arithmetic series

Suppose Arithmetic Series a1+a2+a3+…..an
Then nth term an=a1+(n-1)d

Where
a1- First number of the series
an- Nth Term of the series
n- Total number of terms in the series
d- Difference between two successive numbers

Sum of the total numbers of the arithmetic series

Sn=n/2*(2*a1+(n-1)*d)

Where
Sn – Sum of the total numbers of the series
a1- First number of the series
n- Total number of terms in the series
d- Difference between two successive numbers

Example:

Find n and sum of the numbers in the following series 3 + 6 + 9 + 12 + x?
Here a1=3, d=6-3=3, n=5

x= a1+(n-1)d = 3+(5-1)3 = 15

Sn=n/2*(2a1+(n-1)*d)
Sn=5/2*(2*3+(5-1)3)=5/2*18 = 45

I hope the above formulae are helpful to solve your math problems

 

[jvicens]

related to arithmetic progressions and series.
Thank you for your post about arithmetic progressions and series. I would like to add some additional information and insights about this topic.

Arithmetic progressions and series are not only used in mathematics, but also in many other fields of science such as physics, chemistry, and economics. It is a fundamental concept that helps us understand and analyze patterns and trends in data.

In physics, for example, arithmetic progressions can be used to describe the motion of objects with constant acceleration. This is known as uniformly accelerated motion, where the change in position (displacement) of an object is directly proportional to the square of time.

In chemistry, arithmetic progressions and series can be used to analyze and predict the behavior of chemical reactions. The rate of change of reactants and products over time can be described using this concept.

In economics, arithmetic progressions and series are used to study and forecast economic trends and patterns. For instance, the growth rate of a company's profits over a period of time can be described using an arithmetic progression.

Furthermore, arithmetic progressions and series are not limited to just finite sequences. They can also be used to describe infinite sequences and series, which have many applications in mathematics and other fields of science.

In conclusion, arithmetic progressions and series are important concepts that have a wide range of applications in different fields of science. I hope this information has been helpful and has given you a deeper understanding of this topic. Keep exploring and learning!