Answer:
First Case:
Second Case:
Step-by-step explanation:
We know that the first three terms of an arithmetic series are:
Since this is an arithmetic sequence, each subsequent term is <em>d</em> more than the previous term, where <em>d</em> is our common difference.
Therefore, we can write the second term as;
And, likewise, for the third term:
Let's solve for <em>d</em> for each of the equations.
Subtracting in the first equation yields:
And for the second equation:
To avoid fractions, let's multiply the first equation by 2. Hence:
Therefore:
Simplifying yields:
Solve for <em>p</em>. We can factor:
Factor:
Grouping:
Zero Product Property:
Then, we can use the second equation to solve for <em>d</em>. So:
Substituting:
So, for the first case, <em>p</em> is 5/2 and <em>d</em> is -2.
Likewise, for the second case:
So, for the second case, <em>p </em>is -5/4, and <em>d</em> is 7/4.
By using the values, we can determine our series.
For Case 1, we will have:
17, 15, 13.
For Case 2, we will have:
-11/2, -15/4, -2.
