Q13.

Find the three arithmetic means between 44 and 92.

Verified

Answer

The three arithmetic means between 44 and 92 are 56, 68, 80.

1Step 1. Given Information.

Given there are three arithmetic means between 44 and 92.

2Step 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:

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

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.

3Step 3. Conclusion .

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