Question

The following is a geometric sequence.
-1/2, 1/4, -1/8, 1/16

Answer 1

@Loser66

Answer 2

idk im confuessed

Answer 3

hint:
the ratio between one term and its preceding term is constant, and we can write this:
\[\left( {1/16} \right):\left( { - 1/8} \right) = \left( { - 1/8} \right):\left( {1/4} \right) = \left( {1/4} \right):\left( { - 1/2} \right) = ...?\]

Answer 4

still lost.

Answer 5

hint:
\[\frac{1}{{16}}:\left( { - \frac{1}{8}} \right) = \frac{1}{{16}} \times \left( { - 8} \right) = ...\]

Answer 6

i do.. and @Michele_Laino is it -1/2?

Answer 7

yes! that's right!

Answer 8

so i mutliply each by -1/2?

Answer 9

yes you have to multiply one term by -1/2 in order to get the subsequent term of your geometric sequence

Answer 10

so its only a geometric sequence if its multiply by a fraction?

Answer 11

no, the constant can be also an integer number, or even a irrational number

Answer 12

so is something like
-5,0,5,10 a geometric sequence?

Answer 13

no, it is an arithmetic sequence, since the difference between one term and its preceding term is constant:
0-(-5)= 5-0= 10-5=...?

Answer 14

okay! but what if its like -5,25,-125,625
when its all multiply by -5

Answer 15

it is a geometric sequence whose constant is -5

Answer 16

but why?

Answer 17

because the ration between one term and its preceding term is a constant value

Answer 18

ratio*

Answer 19

okay i get it

Answer 20

ok!