Question

Insert three arithmetic means between 22 and 42

Answer 1

Answer:

The value of "a" is 102

Solution:

Given that,

Sum of 3 arithmetic means between a and 22 is 42

Tow numbers are : a and 22

The primary arithmetic mean is the midpoint between a and 22

\frac{a + 22}{2}

2

a+22

The arithmetic mean between the initial value and the midpoint is

\begin{gathered}\frac{a + \frac{a + 22}{2} }{2}\\\\\frac{3a + 22}{4}\end{gathered}

2

a+

2

a+22

4

3a+22

The arithmetic mean between the midpoint and the final value is

\begin{gathered}\frac{22 + \frac{a + 22}{2} }{2} = 42\\\\\frac{44 +a+22}{4} = 42\\\\66+a = 168\\\\a = 168-66\\\\a = 102\end{gathered}

2

22+

2

a+22

=42

4

44+a+22

=42

66+a=168

a=168−66

a=102

Thus value of "a" is 102

Step-by-step explanation:

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