Question

If A.M of two terms is \[9\] and H.M is \[36\], then G.M. will be
A. \[18\]
B. \[12\]
C. \[16\]
D. None of the above

Answer 1

Hint
The equation \[AM \times HM{\rm{ }} = {\rm{ }}G{M^2}\] can be used to show the relationship between AM, GM, and HM. The arithmetic mean (AM) and the harmonic mean (HM) are multiplied to create the geometric mean (GM). In comparison to HM and AM, GM is worth more than the latter. Compared to AM and GM, HM has a lower value. The geometric mean should be used if the values have different units, as opposed to the arithmetic mean, which is appropriate if the values have the same units. If the data values are ratios of two variables with various measurements, or rates, the harmonic mean is acceptable.
A list of non-negative real numbers has arithmetic means that are greater than or equal to the geometric means of the list. There is only a chance that two means are equal if every number in the list is the same.
Formula used:
\[AM \times HM{\rm{ }} = {\rm{ }}G{M^2}\]
Complete step-by-step solution
To find the value of G.M
The given A.M is equal to \[9\]
\[HM = 36\]
The formula to find the GM is
\[AM \times HM{\rm{ }} = {\rm{ }}G{M^2}\]
\[ = > 9 \times 36\]
\[ = > 324\]
Hence, \[GM = \sqrt {324} \]
\[ = 18\]
Therefore, the correct option is A.
Note
A number series' geometric mean is computed by taking the product of the numbers in the series and raising it to the series' inverse length. The average is determined by adding up all the numbers and then dividing by how many there are in the set of numbers. Take the nth root of the multiplied numbers after multiplying the numbers collectively, where n is the total number of data values.