Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

4, 12, 36, 108, ...

Converges; 484

Diverges

Converges; 52

Converges; 160

@ganeshie8 @phi @beccaboo333

Answer 1

will give best answer & m edal!

Answer 2

if you divide 12/4 you get 3
if you divide 36/12 you get 3
if you divide 108/36 you get 3

Answer 3

First off, have you tried to find the pattern here? It helps to decompose each term into its prime factors and you should be able to notice a pattern.

Answer 4

yes @phi

Answer 5

what do you think the next number is after 108 ?

Answer 6

324

Answer 7

and the number after 324 ?

Answer 8

972

Answer 9

any chance the next number is "closing in" on some number or is it "diverging" ?

Answer 10

i think its closing in on a number

Answer 11

or is it diverginng?

Answer 12

I guess you don't know the definitions these words.
The next number is 3 * the previous number. The next number is bigger than the previous
if we keep going, we get bigger and bigger numbers. If we go far enough we get gigantic enormous humongous numbers.

Answer 13

yes, does that mean it diverges because it doesn't stop at a certain number? or is it converge because its getting bigger?

Answer 14

diverge means we end up with gigantic enormous humongous numbers.

Answer 15

Okay, thank u!

Answer 16

converge means the "next number" is getting closer to some number
example: 1/x
when x =1 we get 1/1 =1
when x = 10 we get 1/10 = 0.1
x=100 , we get 1/100 = 0.01
x=1000000 , we get 0.0000001
get are getting closer and closer to 0
we are converging.

Answer 17

ohhh okay, understood. thank u so much :)

Answer 18

\[\text{Table}\left[4\text{ * }3^{n-1},\{n,1,10\}\right]= \]{4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732}