What is the relation between AP GP and HP?

If the nth term of the arithmetic progression is given by an = a + (n – 1) d, and we know to solve the terms in harmonic progression, we first have to convert the terms of A.P in H.P, so the nth term of the harmonic progression can be given by 1/ a+(n−1)d.

What is AP GP HP series?

Arithmetic Progression (AP) Geometric (GP) and Harmonic Progression (HP): CAT Quantitative Aptitude. Arithmetic Progression, Geometric Progression and Harmonic Progression are interrelated concepts and they are also one of the most difficult topics in Quantitative Aptitude section of Common Admission Test, CAT.

What is the condition for AP?

Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an AP, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1).

What is relation between AM and GM?

The relation between AM GM HM can be represented by the formula AM × HM = GM2. Here the product of the arithmetic mean(AM) and harmonic mean(HM) is equal to the square of the geometric mean(GM).

What is the relation between AM GM and Hm?

AM stands for Arithmetic Mean, GM stands for Geometric Mean, and HM stands for Harmonic Mean. AM, GM and HM are the mean of Arithmetic Progression (AP), Geometric Progression (GP) and Harmonic Progression (HP) respectively.

Can Am GM and HM be equal?

Hint: Here, we will use the formulas for AM, GM and HM of two numbers. Hence, considering all the possibilities we are always getting that both the numbers in the given series are equal to each other. So, in general we can say that all the values are equal in the series where AM=GM=HM.

What is condition for HP?

A series of terms is known as a HP series when the reciprocals of elements are in arithmetic progression. E.g.,1/a, 1/(a+d), 1/(a + 2d), and so on are in HP as a, a + d, a + 2d are in AP. In other words, the inverse of a harmonic sequence follows the rule of an arithmetic progression.

Are am GM and HM in GP?

These three are average or mean of the respective series. AM, GM and HM are the mean of Arithmetic Progression (AP), Geometric Progression (GP) and Harmonic Progression (HP) respectively.

What is the meaning of AM GM HM and GP?

These three are basically the average or mean of the respective series. AM stands for Arithmetic Mean, GM stands for Geometric Mean and HM stands for Harmonic Mean. AM, GM and HM are the mean of Arithmetic Progression (AP), Geometric Progression (GP) and Harmonic Progression (HP).

What is the inequality relation between AM GM and HM?

The inequality relation between AM GM and HM states that the values of AM GM HM are never equal in most of the cases. Among the three means, arithmetic means generally have the highest value. Geometric mean is greater than harmonic mean. However, its value is lesser than the arithmetic mean.

What is the harmonic mean of AM x Hm?

If a, b, c are in HP, then b is the harmonic mean between a and c. If AM, GM and HM be the arithmetic, geometric and harmonic means between a and b, then the following results hold: Therefore, we can write: Or GM 2 = AM x HM…….. (iv)

How do I use AM-GM?

AM-GM can be used fairly frequently to solve Olympiad -level inequality problems, such as those on the USAMO and IMO . See here: Proofs of AM-GM . The weighted form of AM-GM is given by using weighted averages. For example, the weighted arithmetic mean of and with is and the geometric is .