Geometric Progression

Nov 2015
100
1
Kolkata, India
Hi,
I came across a GP questions as follows-
The difference between 5th term and 3rd term of GP is 72. If the 1st term is 1. Find the common ratio.
I had solved it. Please correct me. Where am I wrong?
a= 1 as its the 1st term. ar^4 - ar^2 = 72. This implies r^4- r^2 = 72. From here I can solve r. But the answers are 2, 3, 4 or 5.
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
$a_1r^4 - a_1r^2 = 72$

$a_1=1 \implies r^4 - r^2 - 72 = 0$

$(r^2 - 9)(r^2 + 8) = 0$

$r = \pm 3$

don't agree with 2, 4, and 5
 
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