when two or more arithmetic means are inserted between two arithmetic sequence extreme how are they computed

The answer is below

Explanation:

Given that we need to have two or more arithmetic means inserted between two arithmetic extremes, then we have

d= (an - ak) ÷ ( n - k)

For Example: What are the three arithmetic means of the arithmetic extremes 8 and 16, then a1= 12, and a5= 20?

First we use the formula:

d= (an - ak) ÷ (n - k)

= (20 - 12 ) ÷ (5 - 1)

=> (8) ÷ (4) = 2

Our common difference is 2.

Then we can simply:

a5 = 20

a4 = 20 - 2(1) = 18

a3 = 20 - 2(2) = 16

a2 = 20 - 2(3) = 14

a1 = 20 - 2(4) = 12

Now we have our arithmetic sequence 12, 14, 16, 18, 20

Therefore the three arithmetic means of the arithmetic extremes 12 and 20 ==> 14, 16 and 18.