SOLUTION: The following terms are the beginning of a feometric sequence, where p < 0: 24, -6p, 9pt, -9t Find the value of p and t. I've been stuck on this problem for the last 15 mi

Algebra ->  Sequences-and-series -> SOLUTION: The following terms are the beginning of a feometric sequence, where p < 0: 24, -6p, 9pt, -9t Find the value of p and t. I've been stuck on this problem for the last 15 mi      Log On


   

Question 1037189: The following terms are the beginning of a feometric sequence, where p < 0:
24, -6p, 9pt, -9t
Find the value of p and t.
I've been stuck on this problem for the last 15 minutes and I've had no luck!
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The following terms are the beginning of a feometric sequence, where p < 0:
24, -6p, 9pt, -9t
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The ratio of the second to the first:  %28-6p%29%2F24 = -p%2F4.


The ratio of the third to the second:  %289pt%29%2F%28-6p%29 = %28-3t%2F2%29.


The ratios should be equal:  -p%2F4 = -%283t%29%2F2.


Multiply by -4 both sides. You will get  p = 6t.


The ratio of the fourth to the third:  -%289t%29%2F%289pt%29 = -1%2Fp.


Compare the ratio of -p%2F4 with the ratio of -1%2Fp. It produces p%5E2 = 1. Hence, p = +/-1. Then t = +/-6 correspondingly.


Answer.  p = 1, t = 6   or/and   p = -1, t = -6.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The following terms are the beginning of a feometric sequence, where p < 0:
24, -6p, 9pt, -9t
Find the value of p and t.
I've been stuck on this problem for the last 15 minutes and I've had no luck!
Solutions: 

However, since p < 0, then the only solution is: highlight_green%28matrix%281%2C3%2C+t+=+-+1%2F3%2C+when%2C+p+=+-+2%29%29