Question

Find the next three terms of the sequence. Then write a rule for the sequence.

648, 216, 72, 24

Answer 1

8, 8/3, 8/9
It just divides by three every time

Answer 2

huh

Answer 3

648/3=216
216/3=72
72/3=24
24/3=8
8/3= 2.6
2.6/3=.888
in terms of decimal instead of fractions its
8, 2.6, 0.88

Answer 4

so i just write 8, 2.6,0.88?

Answer 5

the sequence seems to be a geometric progression ....

Answer 6

spose you divide all the numbers there by say 24; what numbers would we get as a result?

Answer 7

648/ 24?

Answer 8

yeah, that should at least get the sequence of numbers to something more readily seen

Answer 9

what should i write down .. just the number or how he should 648/3....

Answer 10

showed*

Answer 11

i get a simpler sequence as:

(648, 216, 72, 24,...)/24 = (27,9,3,1, ...)

27,9,3,1,.... : these numbers follow the same pattern displayed but are easier to work with and notice a working pattern

Answer 12

each new number is 1/3 the previous number; which is the rule for generating the sequence

Answer 13

thats the question tho... =(

Answer 14

working with the simpler set of numbers; do you see a pattern developing? doesnt the setup resemble the 3s times table in reverse?

Answer 15

hmm, prolly not the times table ... but like 3^x seems more suited to it

Answer 16

yes

Answer 17

since
3^3 = 27
3^2 = 9
3^1 = 3
3^0 = 1

lets write this as
\[3^3,3^2,3^1,3^0,...\]
would you agree that a pattern is forming? say the next term is \(3^{-1}\) followed by say \(3^{-2}\) .....

Answer 18

yes

Answer 19

given a previous term \(a_{n-1}\) ;each new term \(a_n\) is formed by dividing the previous term by 3:
\[a_n=\frac13a_{n-1}\]

Answer 20

this is the "rule" that defines the sequence