The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [hint: use a/r, a, and ar to represent the first three terms, respectively.] the three number are and __

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