iheartfood 3 years ago In a geometric sequence, the term an+1 can be smaller than the term an. true or false?

1. irkiz

true

2. irkiz

if n is < 1

3. iheartfood

are u sure?? how did u know so fast?? lol

4. irkiz

as in |n| < 1

5. irkiz

so n ranges from 0 to 1

6. irkiz

oops

7. irkiz

wait

8. iheartfood

oh okay

9. irkiz

if the interval is (-1) that makes it alternating

10. irkiz

so it will be smaller and bigger alternatingly

11. irkiz

(-1)^ 2 is positive, (-2) ^ 3 is negative

12. iheartfood

so this is FALSE?

13. irkiz

(-2)^2 i mean

14. campbell_st

if the common ratio r <1 then each term is smaller that the previous

15. irkiz

there are a few cases yeah. if the sequence convergerges or if the sign alternates

16. iheartfood

wait so its TRUE then???

17. irkiz

yup its true

18. irkiz

i said wait coz my explanation was incomplete

19. iheartfood

oh okay haha :P thanks!!! so its definitely TRUE right?

20. campbell_st

if the absolute value of r is less than 1 |r| < 1 the the geometric series will have a limiting sum...

21. campbell_st

just to clarify things... n is used for the term number... and r is used for the common ratio ( or multiplication constant)... just to avoid confusion.

22. iheartfood

k thanks for all the help y'all!

23. irkiz

yeah. \[ar ^{n}\] if |r| < 1 it converges and if r is negative, it alternates

24. campbell_st

not quite a term in a geometric series is found using \[T_{n} = ar^{n -1}\] n is the term number, T is the Term a is the 1st term and r is the common ratio... please get it right @irkiz

25. iheartfood

k thanks for all the help y'all!