Sequences & Series

Sum of GP to Infinity – Example and Proof

Here you will learn sum of gp to infinity (sum of infinite gp) and its proof with examples. Let’s begin – Sum of GP to Infinity (Sum of Infinite GP) The sum of an infinite GP with first term a and common ratio r(-1 < r < 1 i.e. ,  | r | < 1) …

Formula for Geometric Progression (GP)

Here you will learn what is geometric progression and formula for geometric progression with examples. Let’s begin – Geometric Progression (GP) A sequence of non-zero numbers is called a geometric progression (GP) if the ratio of a term and the term preceding to its always a constant quantity. The constant ratio is called the common …

Formula for Arithmetic Progression (AP)

Here you you will learn what is arithmetic progression (AP) and formula for arithmetic progression. Let’s begin – Arithmetic Progression (AP) A sequence is called an arithmetic progression if the difference of a term and the previous term is always same  i.e.  $$a_{n+1}$$ – $$a_n$$ = constant (=d) for all n $$\in$$ N The constant …

What is AGP – How to Solve AGP Series

Here you will learn what is agp (Arithmetico Geometric Series) and how to solve agp series. Let’s begin – What is AGP (Arithmetico – Geometric series) A series, each term of which is formed by multiplying the corresponding term of an A.P. & G.P. is called the Arithmetico-Geometric Series, e.g. 1 + 3x + 5$$x^2$$ …

Relation Between Arithmetic Geometric and Harmonic mean

Here you will learn formula for arithmetic geometric and harmonic mean and relation between arithmetic geometric and harmonic mean. Let’s begin – Arithmetic Mean Formula If three terms are in A.P. then the middle term is called the A.M. between the other two, so if a, b, c are in A.P., b is A.M. of …

Sum of Harmonic Progression | HP Series

Here you will learn what is harmonic progression (hp) and sum of harmonic progression (hp series). Let’s begin – Sum of Harmonic Progression A sequence is said to be in H.P. if the reciprocal of its terms are in A.P. If the sequence $$a_1$$ + $$a_2$$ + $$a_3$$ + ……… + $$a_n$$ is an HP …

Sum of GP Series Formula | Properties of GP

Here you will learn what is geometric progression (gp) and sum of gp series formula and properties of gp. Let’s begin – Sum of GP Series Formula G.P. is a sequence of non zero numbers each of the succeeding term is equal to the preceding term multiplied by a constant. Thus in GP the ratio …

Formula for Sum of AP Series | Properties of AP

Here, you will learn what is arithmetic progression (ap) and formula for sum of ap series and properties of ap. Let’s begin – The indicated sum of the terms of a sequence. In the case of a finite sequence $$a_1$$, $$a_2$$, $$a_3$$,………,$$a_n$$ the corresponding series is $$a_1$$ + $$a_2$$ + $$a_3$$ + ……… + $$a_n$$ …