What is Arithmetic Progression & Geometric Progression? Video Lecture

What is Arithmetic Progression & Geometric Progression? Video Lecture

About Arithmetic Progression and Geometric Progression

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d".

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio. For example, the sequence 4, -2, 1, - 1/2,.... is a Geometric Progression (GP) for which - 1/2 is the common ratio.

This article on Arithmetic Progression will sprinkle on all the aspects of AP and is helpful for both Class 10 Maths and CA/CMA Foundation Fundamentals of Business Mathematics and Statistics.

 

Properties Of Arithmetic Progression

On the off chance that a similar number is included or deducted from each term of an A.P, at that point, the subsequent terms in the succession are likewise in A.P with similar basic contrast.

In the event that each term in an A.P is divided or multiplied with the equivalent non-zero number, at that point, the subsequent sequence is additionally in an A.P

Three number x, y, and z are in an A.P if 2y=x+z

A sequence is an A.P if its nth term is a linear expression.

In the event that we select terms in the ordinary stretch from an A.P, these chose terms will likewise be in AP.

 

Common Difference In Arithmetic Progression(d)

If a1,a2,a3,…,an is an A.P., then the common difference is given as follows:

d=a2-a1=a3-a2=⋯=an-a(n-1)

Here, d can be positive, negative or zero.

In terms of common difference(d), A.P. can be written as follows:

a,a+d,a+2d,…,a+(n-1)d

Here, a is the first term.

And term of an A.P.

Here,  is the first term,  is a common difference,  refers to the number of terms, and refers to the term.

 

Sum Of N Terms In Arithmetic Progression

For any progression, the sum of n terms can be effectively determined. For an AP, the whole of the principal n terms can be determined if the primary term and the all-out terms are known. The formula for the arithmetic progression sum is explained below:

Sn=n/2[2a+(n-1)d]

This is the AP sum formula to find the sum of n terms in series.

Sum of n terms when the last term (l) is given

S=n/2 (a+l)

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