Question

graph n=6 in the geometric sequence 40, 20, 10, 5 and see if the values will ever become zero or negative?

Answer 1

looks like we need to know the general setup for a geo progression. you know of any?

Answer 2

what do you mean

Answer 3

i mean, there is a general equation that helps us find values for the sequence.

Answer 4

ya it wants me to make that equation

Answer 5

how do we make a geometric sequence? is it something we add to each term? multiply to each term? or something else ....

Answer 6

since its a geometric sequence you multiply somthing to each term to get the value

Answer 7

good, lets start there

we know the 1st term is 40

40*r = 20, what is the value of r?

Answer 8

it can be division to so it 40 divided by 2 is 20 and 20 divided by 2 is 10

Answer 9

so r = 1/2 seems fine

now we have a pattern that develops

40r = 20
40rr = 10
40rrr = 5

40r^(n-1) = nth term

Answer 10

ploting the points on a graph i assume is simple enough to do right? its the 0 or negative part that might be troublesome

Answer 11

yup

Answer 12

what rules or methods do you have to accomplish this with. limit ratio? or some other contraption?

Answer 13

you have to use the equation itself to be able to plot the points since its a geometric you multiplied or divided something to get the values which was 2

Answer 14

right, we plot 1,40 2,20 3,10 4,5 5,2.5 6,1.25

logically, if we have something, and take half of it away .... we still have something left over correct?

Answer 15

ya

Answer 16

then since we will always have something left over, then we never get to zero, or less than 0.

Answer 17

ya but why