Question

Two arithmetic means between 3 and 24 are -

Answer 1

The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

What is arithmetic mean?

Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.  

The two arithmetic means between 3 and 24 are has to be inserted.

3, A₂, A₃, 24

All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:

t(n)=a(n-1)d

Here, d is the common difference a is the first terms and n is the total term.  The first term, a=3 and t₄=24. Thus, the common difference is;

$t(n)=a(n-1)d\\t(4)=3(4-1)d\\24=3(3)d\\24=9d\\d=\dfrac{24}{9}$

The second and 3rd term are:

$A₂=3+\dfrac{24}{9}=\dfrac{51}{9}\\ A₃=\dfrac{51}{9}+\dfrac{24}{9}=\dfrac{75}{9}$

Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

Learn more about the arithmetic mean here;

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