Question

why do the lengths of 3 rectangles with measurements of .5"x.75", 1"x1.5" and 2"x3" form a geometric sequence? how do I write a geometric sequence for these lengths and a recursive or explicit formula for this sequence?

Answer 1

here the rato of their lengths is constant hence the lengths for a geometric sequence)

Answer 2

.5/1=.5 and 1/2 =.5 .75/1.5 =.5 also 1.5/3=.5

Answer 3

So these lengths do make up a geometric sequence? How would I write that sequence?

Answer 4

for gemetric sequence a,ar,ar^2,ar^3......
the nth term in the sequence is written as
a_n=a_1*r^(n-1)
a_n -->> nth term
a_1--> first term
r --> constant ratio

Answer 5

n= number of terms

Answer 6

do I have 6 terms

Answer 7

here u have two geometric sequence

one for length and the other for breadth

Answer 8

is r=.5

Answer 9

for length
a_1 = .75 ,n =3 and r=0.5
for breadth
a_1=0.5,n=3,r=0.5

Answer 10

do i write a recursive or explicit

Answer 11

to write a geometri sequence do I just list the lenghts:.5,1,2 and then do one for the widths:.75, 1.5.3

Answer 12

use
a_n=a_1*r^(n-1)
a_n -->> nth term a_1--> first term r --> constant ratio ,n= number of terms

Answer 13

a sub 3=.75(.5)^(n-1) and a sub 3=.5(.5)^(n-1) Are these correct and are these recursive or explicit formulas?