Determine 5 arithmetic means between 7 and 19.
To insert 5 arithmetic means between 7 and 19, we want to create an arithmetic sequence beginning with 7 and ending with 19 with five terms in between. Hence, the total number of terms is given by .
Remember the formula for the term of an arithmetic sequence is
where is the first term and is the common difference. Now we know that . Therefore, using , we can calculate .
Therefore, we get the 5 arithmetic means between 7 and 19 by iteratively adding 2 to 7 as follows:
Therefore, the five arithmetic means between 7 and 19 are 9, 11, 13, 15, and 17.