Question

1.how do we find arithmetic mean of two arithmetic extremes 2.when two or more arithmetic means arw inserted between two arithmetic extremes, how are they computed? 3.Do infinite sequences have arithmetic means?why?​

Answer 1

Answer:

additive inverse of 0 is

Answer 2

1. how do we find arithmetic mean of two arithmetic extremes

As we know that the arithmetic mean between any two given quantities is half their sum. If more than three terms are in Arithmetic Progress, then the terms between the two extremes are called the arithmetic means between the extreme terms.

One method is to calculate the arithmetic mean. To do this, add up all the values and divide the sum by the number of values. For example, if there are a set of “n” numbers, add the numbers together for example: a + b + c + d and so on. Then divide the sum by “n”.

2. when two or more arithmetic means are inserted between two arithmetic extremes, how are they computed?

When two or more arithmetic means are inserted between two arithmetic extremes, we can simply first use the formula:

 $d=\frac{ an - ak}{ n - k}$

For Example: What are the three arithmetic means of the arithmetic extremes 8 and 16, then , and ?

First we use the formula:

$d=\frac{ an - ak}{ n - k}$

$16 - 8 = 8 = 2$

  5  -  1   4

Our common difference is 2.

Then we can simply:

$a_{5} =16$

$a_{4} = 16 - 2(1) = 14$

$a_3 = 16 - 2(2) = 12$

$a_2 = 16 - 2(3) = 10$

$a_1 = 16 - 2(4) = 8$

Now we have our arithmetic sequence 8, 10, 12, 14, 16

and The three arithmetic means of the arithmetic extremes 8 and 16 are 10, 12, and 14.

3. Do infinite sequences have arithmetic means?why?​

An infinite sequence does not need to be arithmetic or geometric; however, it usually follows some type of rule or pattern. ... The next term in this sequence would be 62 or 36.