If p is the AM of q and r and q is the GM of r and p, then HM between p and q is (a) p^2 (b) pq-

step 1 According to the given problem, I can write the value of p is equal to Q plus r by 2. The value

If p is the AM of q and r and q is the GM of r and p, then...

If $\mathrm{p}$ is the $\mathrm{AM}$ of $\mathrm{q}$ and $\mathrm{r}$ and $\mathrm{q}$ is the $\mathrm{GM}$ of $\mathrm{r}$ and $\mathrm{p}$, then $\mathrm{HM}$ between $\mathrm{p}$ and $\mathrm{q}$ is (a) $\mathrm{p}^{2}$ (b) $\mathrm{pq}-\mathrm{r}$ (c) $\mathrm{r}$ (d) $\mathrm{pq}+\mathrm{r}$

If $\mathrm{p}$ is the $\mathrm{AM}$ of $\mathrm{q}$ and $\mathrm{r}$ and $\mathrm{q}$ is the $\mathrm{GM}$ of $\mathrm{r}$ and $\mathrm{p}$, then $\mathrm{HM}$ between $\mathrm{p}$ and $\mathrm{q}$ is
(a) $\mathrm{p}^{2}$
(b) $\mathrm{pq}-\mathrm{r}$
(c) $\mathrm{r}$
(d) $\mathrm{pq}+\mathrm{r}$

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Key Concepts

Arithmetic Mean (AM)

The arithmetic mean is calculated by summing a set of numbers and then dividing by the count of those numbers. It represents the central value of a dataset and is commonly used as a measure of central tendency in statistics and algebra.

Geometric Mean (GM)

The geometric mean is defined as the nth root of the product of n numbers. It is especially useful in contexts where the values are multiplied together or are exponential in nature, such as growth rates, and it provides a measure that is less affected by extreme values.

Harmonic Mean (HM)

The harmonic mean is found by taking the reciprocal of the arithmetic mean of the reciprocals of the values. It is particularly useful for averaging ratios or rates and emphasizes the influence of smaller values in the dataset.

Relationships Among Means

In many problems, particularly in algebra and statistics, arithmetic, geometric, and harmonic means are compared or related to one another. These relationships can lead to interesting identities or constraints that can be used to solve equations involving unknown quantities.

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