The second term of a geometric Progression is 12 more than the first term. If the common ratio is half of first term, find the third term.

Answer 1

a ar ar^2 ar^3 ar^4

ar - a = 12
r = a/2
so
a (a/2) - a = 12
a^2/2 - a - 12 = 0
a^2 - 2a - 24 = 0
(a-6)(a+4) = 0
a = 6 (or a =-4)
try a = 6, then r = 3
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6 18 54 .... yep, that works :)
try a = -4 then r = -2
-4 8 -16 well that seems to work too