Genevieve is cutting 60-inch piece of ribbon into a ratio of 2:3.Since 2 inches are frayed at one end of the ribbon, she will ne
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Ooh, fun
geometric sequences can be represented as
so the first 3 terms are
the sum is -7/10
and their product is -1/125
from the 2nd equation we can take the cube root of both sides to get
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
subsituting -1/5 for ar
which simplifies to
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for
so
for 2r²-5r+2=0
a=2
b=-5
c=2
so
or 
use them to solve for the value of a
try for r=2 and 1/2
or 
test each
for a=-1/10 and r=2
a+ar+ar²=
it works
for a=-2/5 and r=1/2
a+ar+ar²=
it works
both have the same terms but one is simplified
the 3 numbers are
, 
, and 
geometric sequences can be represented as
so the first 3 terms are
the sum is -7/10
and their product is -1/125
from the 2nd equation we can take the cube root of both sides to get
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
subsituting -1/5 for ar
which simplifies to
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for
so
for 2r²-5r+2=0
a=2
b=-5
c=2
so
use them to solve for the value of a
try for r=2 and 1/2
test each
for a=-1/10 and r=2
a+ar+ar²=
it works
for a=-2/5 and r=1/2
a+ar+ar²=
it works
both have the same terms but one is simplified
the 3 numbers are