SOLUTION: Find the value of p and q in the geometry progression,. 10,p, q, -5/4

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Question 1175713: Find the value of p and q in the geometry progression,. 10,p, q, -5/4
Answer by ikleyn(52780) About Me  (Show Source):
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Find the value of p and q in the geometry progression,. 10,p, q, -5/4
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Geometric progression;  First term is 10;  fourth term is  -5%2F4.


So,  a%5B4%5D = -5%2F4 = 10%2Ar%5E3,  


which implies  r%5E3 = %28%28-5%2F4%29%29%2F10 = -1%2F8;  so  r = -1%2F2.


Thus p = 10%2Ar = 10%2A%28-1%2F2%29 = -5;


     q = 10%2A%28-1%2F2%29%5E2 = 10%2F4 = 5%2F2.


ANSWER.  p = -5;  q = 5%2F2.

Solved.