Question

A.M. G.M H.m.of the number 4 and 16​

Answer 1

Note:

1) A.P. stands for Arithmetic Progression. This is a type of sequence in which the difference between the two consecutive terms is constant.

2) G.P. stands for Geometric Progression.This is a type of sequence in which the ratio between the two consecutive terms is constant.

3) H.P. stands for Harmonic progression. This is a type of sequence in which the reciprocals of its terms are in A.P.

4) A.M. (Arithmetic mean) of two numbers a and b is given by ;

A.M. = (a+b)/2

5) G.M. ( Geometric mean) of two numbers a and b is given by ;

G.M. = √(ab)

6) H.M. (Harmonic mean) of two numbers a and b is given by ;

H.M. = 2ab/(a+b)

Here,

The given numbers are 4 and 16.

Thus,

A.M. = (4+16)/2 = 20/2 = 10

G.M. = √(4•16) = 2•4 = 8

H.M. = 2•4•16/(4+16)=2•4•16/20=32/5

Hence,

A.M. of 4 and 16 is 10.

G.M. of 4 and 16 is 8.

H.M. of 4 and 16 is 32/5.

Answer 2

Answer:

By applying formula of finding Arithmetic mean between two numbers a and b we can find A.M as

$A.M. = \frac{a + b}{2} \\ = </p><p> \frac{4 + 16}{2} \\ = \frac{20}{2} \\ = 10$

To find Geometric mean between 4 and 16 we can use the formula of finding Geometric mean between a and b that is

$G.M. = \sqrt{ab} \\ = \sqrt{16 \times 4} \\ = \sqrt{64} \\ </p><p> = 8$

Harmonic mean between 4 and 16 can be calculated using formula to find between that is

$H.M = \frac{2ab}{a + b} \\ = \frac{2 \times 16 \times 4}{16 + 4} \\ = \frac{128}{20} \\ = \frac{32}{5}$