Question

Which of the following sequences represents a geometric sequence? -3, -6, -12, -24, ... 1, 4, 9, 16, ... -1, 2, 5, 8, ... 0, 2, 4, 6, ...

pllllleeeaaassseee help

Answer 1

we know that
In a Geometric Sequence, each term is found by multiplying the previous term by a constant
so

case 1) -3, -6, -12, -24
let
a1=-3
a2=-6
a3=-12
a4=-24
a2/a1=-6/-3-----> 2----------> a2=a1*(2)
a3/a2=-12/-6----> 2--------> a3=a2*(2)
a4/a3=-24/-12---> 2--------> a4=a3*(2)
This sequence has a factor of 2 between each number.Each term (except the first term) is found by multiplying the previous term by 2the term 2 is called the common ratio
so
the rule is

`an=a1*2^{(n-1)`
Is a Geometric Sequence

case 2) 1, 4, 9, 16
Let
a1=1
a2=4
a3=9
a4=16
so
a1=1²-----> 1
a2=2²----> 4
a3=3²----> 9
a4=4²----> 16
the rule is

`an=n^(2)`
Is not a Geometric Sequence

case 3) -1, 2, 5, 8,
let
a1=-1
a2=2
a3=5
a4=8
a2-a1=2-(-1)------> 3-------> a2=a1+3
a3-a2=5-2-------> 3-------> a3=a2+3
a4-a3=8-5-------> 3------> a4=a3+3
the rule is

`an=a1+3*(n-1)`
Is not a Geometric Sequence, is an Arithmetic Sequence

case 4) 0, 2, 4, 6,
Let
a1=0
a2=2
a3=4
a4=6
a2-a1=2-0------> 2-------> a2=a1+2
a3-a2=4-2-------> 2-------> a3=a2+2
a4-a3=6-4-------> 2------> a4=a3+2
the rule is

`an=a1+2*(n-1)`
Is not a Geometric Sequence, is an Arithmetic Sequence

therefore

the answer is
The sequence -3, -6, -12, -24 is a Geometric Sequence