Sequence problems?? I got a solution...

[arabiannight975]

well people in the math book for IGCSE there is no specified formula for finiding the sequence......
well its one of the most hardest thing to do in the paper...
I recently came to know about Geometric progression and arthematic progression!!

In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

Sequence = a + (n - 1)d,


Geometric

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. The sum of the terms of a geometric progression is known as a geometric series.

The n-th term of a geometric sequence with initial value a and common ratio r is given by

a_n = a*r^{n-1}.

 

[Saturation]

Thanks! But what do you mean in GEOMETRIC, "initial value a" ?

 

[arabiannight975]

Well its means the initial value..!!
the value of the first term!

 

[Saturation]

Ok i tried that but i still dont get it...
CAn you please show it to me, by using the sequence 2, 6, 18, 54?
I know common ratio is 3 here, so r= 3

can u please explain after that?

THnank you!

 

[Pierre Samy]

will thats good one
buti think u made one mistake in the second formula how
A_N= a*r^{n-1}. ( i mean the underscore )

 

[arabiannight975]

Ok i tried that but i still dont get it...
CAn you please show it to me, by using the sequence 2, 6, 18, 54?
I know common ratio is 3 here, so r= 3

can u please explain after that?

THnank you!

Well the formula is a*r^(n-1)

and now the first value is sequence is 2 so a=2 Ratio (r)=3

so it will be 2*3^(n-1)

this is your nth formula...

lets keep n=3

so= 2*3^(3-1)
= 2*3^2
=18.


This is how it will be solved....
if you need anything else let me know!

 

[Saturation]

Ohhh! Okk!! I got it now! thank you!
Good luck for tomorow!

 

[dotcom]

how about the square and cube sequence? is there any specific formula for any of them?
i.e: 2,4,16,256,65536

 

[PlanetMaster]

This is a geometric progression.
A geometric progression is a sequence where each term is r times larger than the previous term. r is known as the common ratio of the sequence. The nth term of a geometric progression, where a is the first term and r is the common ratio, is ar^(n-1)

For example, in the following geometric progression, the first term is 1, and the common ratio is 2:
1, 2, 4, 8, 16, ...

The nth term is therefore 2^(n-1)

The sum of the first n terms of a geometric progression is:
a(1 - r^n )
....1 – r

 

[Ahmed-Azurus]

new formula for me to learn but i never needed it yet..
i think they will surprise us in less than 12 hours
thx planet master

 

[Pierre Samy]

thanks for the sequence help
but still there is 2 more formulaes missing
one of them is for square and cubic number
planet master ig ot a complain about the site that it laggs during the afternoon time where too many users log in and the servers is over loaded....
thanks for help and sorry for complains

 

[Pierre Samy]

Mister Dotcom the example u have given have brought me a heachae and i mean it cuz i though i have learnt how to solve any sequence but i didnt find any solution for ur example just to find that there is no Nth term for such a sequence in order to get or find Nth term u need to have neutral number or commom ratio and your example conatins neither of both so the examnier can never ask u find the Nth term he can only say find the next 2 term whcih is 65536^2 and and of 65536^2 is then squared agin in order to get the next and last term
hope it help good luck people

 

[PlanetMaster]

thanks for the sequence help
but still there is 2 more formulaes missing
one of them is for square and cubic number

The formula is the same.
The common ratio is squared or cubed.
I don't think that geometric progression is in IGCSE syllabus but it many marking schemes, the method shown is geometric progression.''

planet master ig ot a complain about the site that it laggs during the afternoon time where too many users log in and the servers is over loaded....
thanks for help and sorry for complains

I'm aware of that!
Its a routing problem due to maintenance.
Replacing server's can take more than a week during which site will remain dead.
So waiting should be the best option for now.

 

[arabiannight975]

Well I tried to solve that sequence you gave and conquered it aswell

It will be solved by the EXACT same formulas but in a different way!!

2,4,16,256

well if you take a common denominator it will be 2

after that you can rasie the power of 2..


so it will be 2^1 , 2^2 , 2^4 , 2^8

NOw if you look closely...
the power of the 2 has the same ratio........ 1,2,4,8,.........which is 2..

so you can use the geometric progression...

so the anwser will be

2^((2)^n-1)


so lets keep 3 as the nth tern

2^((2)^3-1)

answer will be 16!!