Question

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

648, 216, 72, 24

Answer 1

my answer was

8,8/3,8/9





x(n)=x(n-1)/3

Answer 2

yes, that looks right
good job :)

Answer 3

youre right with the sequence however rule will be a/(3^(n-1)) where a = 648

Answer 4

and nice recursive formula

Answer 5

but my teacher says its wrong or incomplete

Answer 6

maybe your teacher wants you to simplify 8/3?
maybe your teacher wants you to give the formula @Meinme gave

Answer 7

@LilySwan as i said the formula u dervied wont work everywhere in the series

Answer 8

its a geometric progression

Answer 9

yeah its not Arithmetic progression its geometric because theres a common ratio not common difference

Answer 10

so @LilySwan do you know how to find the equation of the sequence?

Answer 11

my teacher commented this
You've given me a recursive formula. For your rule think about what you are doing each time. How should that be expressed in the rule?

Answer 12

yes, that makes sense. what the teacher wants you to do is find the formula that applies your recursive formula to the first value a variable number of times

Answer 13

right!!

Answer 14

the general formula of a geometric sequence is a*r^(n-1)

Answer 15

a is the first term
r is what you multiply by each time to get the next term, this is what you found in your recursive formula
n is which term it is, (it is n-1 because a is the first term instead of term 0)

Answer 16

are you confused?

Answer 17

very much

Answer 18

sorry

Answer 19

@LilySwan Is r = 1/3 ?

Is the common ratio 1/3? Each term is 3 times the one preceeding it?

So, 216 = 1/3*648 and so on?

Answer 20

http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

Answer 21

this should help you be less confused

Answer 22

@Directrix yes, we already got that

Answer 23

@LilySwan does the link help?

Answer 24

a bit

Answer 25

g(n) = 648* (1/3)^(n-1) = 2^3 * 3^4 * [(3)^(-1)]^(n-1) = 2^3*3^4*((3^(-1))^(n-1)=

2^3 * 3^(4) * ((3^(-1(n-1)) = 2^3 * 3 ^ (4 + (-n+1) = 8 * 3 ^ (5 - n)

@LilySwan
8 * 3 ^ (5 - n) --> This is probably what the teacher wants to see.-->