Скачать или смотреть Introduction to Arithmetic Progression (A.P) and Geometric Progression (G.P) Sequence || Formulas

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In this video, we will discuss Arithmetic Progression (A. P) and Geometric Progression (G. P).

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"
For example, the sequence 2, 4, 6, 8... is an arithmetic progression with 2 as the common difference. The progression 5, 10, 15, 20...is an Arithmetic Progression (AP) with 5 as the common difference.

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tn = nth term and a = first term. Here d = common difference = d2 -d1.

Sum of first n terms of an AP: S =(n/2)[2a + (n- 1)d]

When three quantities are in AP, the middle one is called as the arithmetic mean of the other two. If a, b and c are three terms in AP then b = (a+c)/2

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.

The general form of a GP is a, ar, ar2, ar3 and so on.

a is the first term, r is the common ratio of a finite
#ap #gp #arithmeticprogression #geometricprogression #maths #mathematics