The explicit formula for the geometric sequence
is

Step-by-step explanation:
The formula of the nth term of a geometric sequence is
, where:
- a is the first term of the sequence
- r is the common ratio between the consecutive terms
The geometric sequence of
is 6 , -2 ,
,
, 
∵
= 6
∵ 
∵
= -2
∴ 
- Divide both term by 2 to simplify it
∴ 
∵ 
- Substitute the value of
and r in the rule above
∴ 
The explicit formula for the geometric sequence
is

Learn more:
You can learn more about the geometric sequence in brainly.com/question/1522572
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Edit
Consecutive integers are 1 apart
x,x+1,x+2
(x)(x+1)(x+2)=-120
x^3+3x^2+3x=-120
add 120 to both sides
x^3+3x^2+3x+120=0
factor
(x+6)(x^2-3x+20)=0
set each to zero
x+6=0
x=-6
x^2-3x+20=0
will yeild non-real result, discard
x=-6
x+1=-5
x+2=-4
the numbers are -4,-5,-6
use trial and error and logic
factor 120
120=2*2*2*3*5
how can we rearange these numbers in (x)(y)(z) format such that they multiply to 120?
obviously, the 5 has to stay since 2*5=10 which is out of range
so 2*2*2*3 has to arrange to get 3,4 or 4, 6 or 6,7
obviously, 7 cannot happen since it is prime
3 and 4 results in in 12, but 2*2*2*3=24
therfor answer is 4 and 6
they are all negative since negaive cancel except 1
the numbers are -4,-5,-6