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
Q^2 - 125 = 0
q^2 = 125
q = +/- sqrt 125 = 11.18, -11.18
The answer is (C). All sides and angles of the square is equal. Its diagonals bisect each other and meet at 90°. If two lines are said to meet at 90°, these lines are perpendicular to each other. Therefore, the diagonals of a square is perpendicular to each other
It will just be -7/12 because anything times 1 stays the same
Answer: Use this rule to change the term to a radical:
x
1
n
=
n
√
x
18
1
2
⇒
2
√
18
⇒
√
18
We can simplify this expression, if necessary, by using this rule for radicals:
√
a
⋅
b
=
√
a
⋅
√
b
√
18
⇒
√
9
⋅
2
⇒
√
9
⋅
√
2
⇒
3
√
2
Step-by-step explanation: