Question

Find three real geometric means between 1/525 and 25/21

Answer 1

if we write out the sequence like this

g1 m1 m2 m3 g5

Answer 2

then we can reconstruct it by knowing the formula for a geometric series

Answer 3

gn = g1 * r^(n-1)

gn/g1 = r^(n-1)

(n-1)rt of (gn/g1) = r

Answer 4

when the (n-1) part gets larger than 3 its prolly easier to use the exponential notation:\[\large r=\left(\frac{g_n}{g_1}\right)^{(\frac{1}{n-1})}\]

Answer 5

ok how do plug these in

Answer 6

define your gn and your g1 with the values given; since n=5 in this case, id use a 5 in place of n

Answer 7

ok 5n

Answer 8

whats g1

Answer 9

g5 = 1/525 ; g1 = 25/21
or
g1 = 1/525 ; g5 = 25/21

it doesnt matter which is which, as long as we are consistent thruout

Answer 10

if we pick the first option:

g5 = 1/525 ; g1 = 25/21 .... i get an r value of 5

Answer 11

g2 = g1 * r^1
g3 = g1 * r^2
g4 = g1 * r^3

which then would give us

g2 = 25/21 * 5^1
g3 = 25/21 * 5^2
g4 = 25/21 * 5^3

Answer 12

so do we multiply

Answer 13

make that r = 1/5 if we go that route ....

Answer 14

yes, we multiply after we set it all up. im sure that there is a simpler way to go about it, but i never remember it ....

Answer 15

92=5.95

Answer 16

g2=29.76

Answer 17

g4=148.8

Answer 18

i made a mistake in the "r" with my setup; try using this instead

g2 = 25/21 * 1/5^1
g3 = 25/21 * 1/5^2
g4 = 25/21 * 1/5^3

Answer 19

isn't it the same

Answer 20

oh no ok

Answer 21

no, multipling stuff by "5" is not the same as multiplying stuff by "1/5"

Answer 22

g2=.2380
g3=.0476
g4=.0095

Answer 23

that looks better to me; just be sure they want it in decimal form before submitting; else keep it in fractions

Answer 24

ok thanks