Question

insert five(5) geometric means between :
1) 4 & 49
2) square root of 3 & 9
3) 1 over two & 32
4) 2 & 54

i need this to my homework .. please Help me .. :))

thanks .

Answer 1

I am not sure what is meant by "insert five", but the geometric mean of two numbers \(a\) and \(b\) is given by \(\sqrt{ab}\).

Answer 2

im sorry i dont know too .. my adviser just give the problem to us ..

Answer 3

Well, two numbers cannot have more than one geometric mean. I'd just evaluate the geometric means of the given pairs of numbers.

Answer 4

ok .

Answer 5

ok .

Answer 6

please read this . where are u ?

Answer 7

I can't help you unless you ask a question.

Answer 8

ok . i mean its not geometric .. its arithmetic .

Answer 9

The arithmetic mean is \[\frac{a+b}{2}\]whereas the geometric mean is \[\sqrt{ab}.\]Either way, it's just evaluating the formula.

Answer 10

OMG how can answer it i dont know it ......... thanks to your help ..

Answer 11

Let me give you an example. Take the numbers 2 and 3. Their arithmetic mean is\[\frac{2+3}{2} = \frac{5}{2}.\]Their geometric mean is \[\sqrt{2 \cdot 3} = \sqrt{6}.\]

Answer 12

my adviser teach us arithmetic like this ............
the difference is equals to 3 :

3, 6 , 9 , ... and so on ..

what do u think ?

Answer 13

That is an arithmetic series, which is distinct from an arithmetic mean. You wrote geometric mean in your question.

Answer 14

ohh .. yes i remember its arithmetic series , thanks for remind me :))

Answer 15

can u answer it .. ??

Answer 16

I still do not understand what you are asking. The question you wrote doesn't make sense.

Answer 17

ok . i dont have my chance ......

Answer 18

i dont know it .. i PROMISE !!!!

Answer 19

@yakeyglee Here's what I think they mean: for example, insert 3 means between 2 and 32 would mean the result is 4, 8, 16

Answer 20

yes .. your right @whpalmer4 .

Answer 21

thats what i mean so .

Answer 22

hey !!

Answer 23

Okay, so if you have two numbers \(x,y\) and you want to insert \(n\) geometric means, you find the common ratio by taking \[\frac yx = a^{n+1}\] and solving for \(a\). For my example of 3 means between 2 and 32,
\[\frac{32}{2} = a^{3+1}\]\[16=a^4\]\[a=2\]So our numbers are 2, 4, 8, 16, 32

Answer 24

For the first problem, \[\frac{49}{4} = a^{5+1}\]\[a=\sqrt[6]{\frac{49}4}\approx 1.51829\]So the values of the sequence would be
4,6.07318, 9.22087, 14, 21.2561, 32.2731, 49