If p-3, p+3, 4p+3 are three consecutive terms of a geometric progression, find the possible values of p and the corresponding value of the common ratio.

Step-by-step explanation:

hello :

look this solution :

 p = 6, r = 3       or       p = -1,  r = -1/2

Step-by-step explanation:

Since p - 3, p + 3, and 4p + 3 are consecutive terms in a geometric progression, then the proportion of the 2nd term over the 1st equals the 3rd term over the 2nd term.

Step 1 is to find p.

I will show that 3 is not valid below

Step 2 is to find r (common ratio).

Check:

               p = 6                                    p = -1    

p - 3:       6 - 3 = 3                              -1 - 3 = -4

p + 3:      6 + 3 = 9                             -1 + 3 = 2

4p + 3:    4(6) + 3 = 27                      4(-1) + 3 = -1

3(3) = 9                                         -4(-1/2) = 2

9(3) = 27                                        2(-1/2) = -1