Question

In a geometric sequence, the term an+1 can be smaller than the term an.

true or false?

Answer 1

true

Answer 2

if n is < 1

Answer 3

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

Answer 4

as in |n| < 1

Answer 5

so n ranges from 0 to 1

Answer 6

oops

Answer 7

wait

Answer 8

oh okay

Answer 9

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

Answer 10

so it will be smaller and bigger alternatingly

Answer 11

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

Answer 12

so this is FALSE?

Answer 13

(-2)^2 i mean

Answer 14

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

Answer 15

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

Answer 16

wait so its TRUE then???

Answer 17

yup its true

Answer 18

i said wait coz my explanation was incomplete

Answer 19

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

Answer 20

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

Answer 21

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.

Answer 22

k thanks for all the help y'all!

Answer 23

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

Answer 24

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

Answer 25

k thanks for all the help y'all!