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# Nth term formulas

+1
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9
+597

hi guys,

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

Nov 21, 2019

#1
+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
+597
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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
+105989
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Hi Juriemagic,

It is good to see you again.

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
+105989
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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.

Nov 21, 2019
edited by Melody  Nov 21, 2019
#6
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Hello sweet Melody!!!..

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
+105989
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hi again Juriemagic,

I am very flattered by your term of endearment.

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
+597
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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
+28289
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See  https://en.wikipedia.org/wiki/Fibonacci_number for a closed form expression for the Fibonacci sequence,

Nov 21, 2019
#9
+597
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Thanks Alan, will check it out..

juriemagic  Nov 21, 2019