SOLUTION: The first three terms of a GP are p-5,2p-6 and 4p-5.Determine: 1.The value of p. 2.The sum of the values.

Algebra ->  Sequences-and-series -> SOLUTION: The first three terms of a GP are p-5,2p-6 and 4p-5.Determine: 1.The value of p. 2.The sum of the values.      Log On


   

Question 1182616: The first three terms of a GP are p-5,2p-6 and 4p-5.Determine:
1.The value of p.
2.The sum of the values.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In a GP, the ratio of consecutive terms is constant:

%282p-6%29%2F%28p-5%29=%284p-5%29%2F%282p-6%29

Cross multiplying gives

%284p-5%29%28p-5%29=%282p-6%29%282p-6%29

Note a slightly faster way to get to that equation is to use the fact that, for any three consecutive terms of a GP, the product of the first and third is the square of the second:

%284p-5%29%28p-5%29=%282p-6%29%5E2

Continuing....

4p%5E2-25p%2B25=4p%5E2-24p%2B36
-11+=+p

1. ANSWER: p = -11

The three terms are
p-5 = -16
2p-6 = -28
4p-5 = -49

We can verify that those numbers form a GP:
-28/-16 = 7/4
-49/-28 = 7/4

2. ANSWER: the sum of the three terms is (-16)+(-28)+(-49)=-93