## anonymous one year ago The following is a geometric sequence. -1/2, 1/4, -1/8, 1/16

1. anonymous

@Loser66

2. anonymous

idk im confuessed

3. Michele_Laino

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

4. anonymous

still lost.

5. Michele_Laino

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

6. anonymous

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

7. Michele_Laino

yes! that's right!

8. anonymous

so i mutliply each by -1/2?

9. Michele_Laino

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

10. anonymous

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

11. Michele_Laino

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

12. anonymous

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

13. Michele_Laino

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

14. anonymous

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

15. Michele_Laino

it is a geometric sequence whose constant is -5

16. anonymous

but why?

17. Michele_Laino

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

18. Michele_Laino

ratio*

19. anonymous

okay i get it

20. Michele_Laino

ok!