The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate the common difference for each value of p.

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 d more than the previous term, where d is our common difference.

Therefore, we can write the second term as;

And, likewise, for the third term:

Let's solve for d 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 p. We can factor:

Factor:

Grouping:

Zero Product Property:

Then, we can use the second equation to solve for d. So:

Substituting:

So, for the first case, p is 5/2 and d is -2.

Likewise, for the second case:

So, for the second case, p is -5/4, and d 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.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

false

step-by-step explanation:

false.   two legs of the trapezoid would be congruent, but the other two would not.   were all the legs congruent, then we'd have a square; were the 2 shorter sides congruent and the 2 longer sides also congruent, we'd have a rectangle.