Geometric Sequences

[HNO]

Sept 15th 2012

Given the geometric 7, 7/2, 7/4

I found the ration which is .5!

I am then asked to: Find term 5 by using the recursive formula

THE RECURSIVE FORMULA is >>>tn= (tn - 1)r

I know that term 5 is .4375 because I found term for and multiplied that by the ratio ( .875 X 0.5)= .4375

Im am unsure if I'm suppose to plus term 4 in tn? this is what Im confused

if I do so….

tn = (.875 - 1) .5

.875-1 = -.125 do I put this to the other side or multiply by 5

Hope this makes sense (=

 

[Yogi]

Sept 15th 2012

Given the geometric 7, 7/2, 7/4

I found the ration which is .5!

I am then asked to: Find term 5 by using the recursive formula

THE RECURSIVE FORMULA is >>>tn= (tn - 1)r

I know that term 5 is .4375 because I found term for and multiplied that by the ratio ( .875 X 0.5)= .4375

Im am unsure if I'm suppose to plus term 4 in tn? this is what Im confused

if I do so….

tn = (.875 - 1) .5

.875-1 = -.125 do I put this to the other side or multiply by 5

Hope this makes sense (=

It should be \(\displaystyle t_n= (t_{n - 1})r\)
When n is 5, \(\displaystyle t_{n-1}\) is the 4th term.

 

[HNO]

It should be \(\displaystyle t_n= (t_{n - 1})r\)
When n is 5, \(\displaystyle t_{n-1}\) is the 4th term.

Hi Yogi!

So then I would write:

tn= (.875 - 1).5

If I punch this all in my calculator I get -.0625

What am i doing wrong?

 

[HallsofIvy]

Hi Yogi!

So then I would write:

tn= (.875 - 1).5

If I punch this all in my calculator I get -.0625

What am i doing wrong?

NO! The "-1" is in the subcript: \(\displaystyle t_n= rt_{n-1}\) so that, as Yogi told you, if n= 5, n-1= 4. \(\displaystyle t_5= .5t_4\)

That is, your sequence is 7, 7/2, 7/4, each time multiplying by 1/2. I, personally, wouldn't use the decimal form, .5. I would just continue the sequence as 7, 7/2, 7/4, 7/8, 7/16, 7/32, 7/64, ....

 

[HNO]

NO! The "-1" is in the subcript: \(\displaystyle t_n= rt_{n-1}\) so that, as Yogi told you, if n= 5, n-1= 4. \(\displaystyle t_5= .5t_4\)

That is, your sequence is 7, 7/2, 7/4, each time multiplying by 1/2. I, personally, wouldn't use the decimal form, .5. I would just continue the sequence as 7, 7/2, 7/4, 7/8, 7/16, 7/32, 7/64, ....

I know that each time you multiply by .5 to get it. But my teacher wants me to show him plunking it into his formula

(5-1).5

tn (t4) = .875 x .5

Is this all I would need to write then

 

[HallsofIvy]

I know that each time you multiply by .5 to get it. But my teacher wants me to show him plunking it into his formula

"multiply by .5" is exactly what that formula says!

(5-1).5

You are either being very sloppy (fatal in mathematics) or still do not understand. "5- 1" is the index on the "t". You are NOT multiplying "5- 1" by .5.

tn (t4) = .875 x .5

Is this all I would need to write then

Well, you should say where you got the ".875"! Also, that is the fourth term and you were asked to find the fifth term.

 

[HNO]

"multiply by .5" is exactly what that formula says!


You are either being very sloppy (fatal in mathematics) or still do not understand. "5- 1" is the index on the "t". You are NOT multiplying "5- 1" by .5.


Well, you should say where you got the ".875"! Also, that is the fourth term and you were asked to find the fifth term.

(5-1).5 = 2

I'm sorry If I am slopping (Kinda makes me feel bad) Usually I'm not but its hard for me to do math on the computer

I got my answer by multiplying .875 x .5 = .4375

But he wants us to plug it into the recursive formula

tn = (tn-1)r

if you could just step by step what goes in where …. what goes in tn ? because I am looking for Tn?

I'm sorry I am just really confused and probably over thinking things :/

 

[HallsofIvy]

You are consistently refusing to do what is suggested! The equation does NOT say
"tn-1", which would be interpreted as "t times n minus 1", it says "t_(n-1)". The fact that the "n-1" is a subscript is crucial to understanding the formula- its says that to find each term (after the first which is given), you multiply the previous term by .5.

t_1= 7 (given)

t_2= 7(.5)= 3.5 (or 7(1/2)= 7/2)

t_3= 3.5(.5)= 1.75 (or (7/2)(1/2)= 7/4)

t_4= 1.75(.5)= 0.875 (or (7/4)(1/2)= 7/8)

t_5= 0.75(.5)= ?