Question

Find the three arithmetic means between 44 and 92.

Short answer

The three arithmetic means between 44 and 92 are56, 68, 80.

Step-by-step solution

Step 1. Given Information.

Given there are three arithmetic means between 44 and 92.

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$.

Since there are three arithmetic means between 44 and 92,

The first term is $a_1=44$

And the fifth term is $a_5=92$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_5=a_1+(5-1)d\\ 92=44+4d\\ 4d=92-44\\ 4d=48\\ d=12\end{array}$

Hence the common difference is 12.

Since the first term in the arithmetic sequence is 44:

The next term in the arithmetic sequence is $44+12=56$

The next term in the arithmetic sequence is $56+12=68$

The next term in the arithmetic sequence is $68+12=80$

And the fifth term in the arithmetic sequence is 92.

Step 3. Conclusion.

Hence, the three arithmetic means between 44 and 92 are 56, 68, 90.