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avatar+597 

hi guys,

 

please help me and teach me PLEASE how to go about calculating the nth term formulas for these patterns.

 

T1 = 1

T2 = 1

T3 = 2

T4 = 3

T5 = 5

 

and for this one:

 

T1 = 1

T2 = 4

T3 = 16

T4 = 25

 

and the last one

 

T1 = 1

T2 = 8

T3 = 27

T4 = 64

T5 = 125

 

I have really tried them all...just cannot crack them...please help me with this...

 Nov 21, 2019
 #1
avatar
+1

1) 

The first one is the Fibonacci sequence; Each new term is the SUM of previous two terms. So, next few terms are:

3 + 5 =8, 5 + 8 =13, 8 + 13 =21.......and so on.

 

2)

This one consists of the SQUARES of counting numbers:

1^2, 2^2, 3^2, 4^2, 5^2..........1, 4, 9, 16, 25........etc.

 

3)This one consists of the CUBES of counting numbers:

1^3, 2^3, 3^3, 4^3, 5^3..........1, 8, 27, 64, 125.......etc.

 Nov 21, 2019
 #2
avatar+597 
+1

Hi guest,

 

i do appreciate your response, however my problem really is how to calculate for example the 10th term for each of these sequences. I struggle to put together a formula..

 

The 3rd sequence I gave, i finnaly got...it's just Tn = n^3

juriemagic  Nov 21, 2019
edited by juriemagic  Nov 21, 2019
 #3
avatar+105989 
+1

Hi Juriemagic,

It is good to see you again.  cool

 

T1 = 1

T2 = 1

T3 = 2

T4 = 3

T5 = 5

 

This is the fibonacci sequence.

I actually do not know how to express the nth term of this sequence in a nice neat way

Obviously   

 

\(T_1=1\\ T_2=1\\ \text{Where n >2 and n is an integer}\\ T_n=T_{n-1}-T_{n-2}\)

 

I suspect you need somthing easier to use than that.  Am I right or is that all you want?

 Nov 21, 2019
 #4
avatar+105989 
+2

and the 3rd one

 

T1 = 1

T2 = 8

T3 = 27

T4 = 64

T5 = 125

 

These are just cubic numbers.  Can you do it yourself now?

 

The second sequence is just as easy.  

 

I just takes practice, you will get the hang of these.  cool

 Nov 21, 2019
edited by Melody  Nov 21, 2019
 #6
avatar+597 
+1

Hello sweet Melody!!!..smiley

 

oops, won't say that again..., but I WANTED to....

 

The 1st sequence is Fibonacci yes, I googled on that but there does not seem to be a mathematical layterm solution for it, 

 

The 2nd sequence is a problem,

T1 = n,

T2 = n^2

T3 = (n+1)^2

T4 = (n+1)^2

T5 = n^2

 

So, I cannot determine a nth term rule....say, for the 10th term?

 

The 3rd sequence I've got sorted....thank you sooo much for assisting...

juriemagic  Nov 21, 2019
 #7
avatar+105989 
+1

 

hi again Juriemagic,

I am very flattered by your term of endearment.  wink

I expect a lot of people here would think you have a little sunstroke though.   LOL.

 

 

I think you have a copy error in the original question

 

T1 = 1     =1^2

T2 = 4      =2^2

Ahr there is a mistake, I am pretty sure that  T3 was supposed to be  9    = 3^2

 

T4 = 16    =4^2

T5=25      =5^2

 

Tn = n^2

Melody  Nov 21, 2019
 #8
avatar+597 
+1

laughlaughlaugh

 

Thank you Melody...I'm sure it must have been a pelling error. .....spelling error...lol....Stay well untill next time!

juriemagic  Nov 21, 2019
 #5
avatar+28289 
+3

See  https://en.wikipedia.org/wiki/Fibonacci_number for a closed form expression for the Fibonacci sequence,

 Nov 21, 2019
 #9
avatar+597 
+1

Thanks Alan, will check it out..

juriemagic  Nov 21, 2019

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