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Find out the wrong number in the given sequence of

Schüler

Tags: Mathematik

RASTA aktiv_icon

23:28 Uhr, 23.11.2022

Tag!

Find out the wrong number in the given sequence of numbers.

8, 13, 21, 32, 47, 63, 83

Well, I tried to see if this is a geometric sequence but it is not, because I don't see there is a common ratio among the numbers listed.
Also, I tried the arithmetic sequence, and found no common difference here,
Any lead will be appreciated, thanks in advance!.

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HAL9000

23:42 Uhr, 23.11.2022

Replace 47 with 46 and then it's a quadratic sequence.

Verified by iterated differences:

zero order (original sequence): 8,13,21,32,46,63,83
first order: 5,8,11,14,17,20
second order: 3,3,3,3,3

RASTA aktiv_icon

23:56 Uhr, 23.11.2022

Thanks a lot, my friend. that is good!.Richtig gut!

HAL9000

09:11 Uhr, 24.11.2022

associated quadratic function:

f (n) = \frac{3 n^{2} + n + 12}{2}

for

n = 1, 2, \dots, 7

RASTA aktiv_icon

21:17 Uhr, 24.11.2022

Hello, I have one question. I have been trying to find the nth number for this quadratic sequence but I am not getting anywhere, could you help?
I know that the first difference is

5 + 8 + 11 + 14 + 17 + 20

and that the second difference is

+ 3 + 3 + 3 + 3 + 3

i

know this is a quadratic sequence because the second difference is the same, so it should

start off at

n^{2}

I have seen videos where the second difference is even. then the tutor says to have the number

and put it in front of

n,

let's suppose the second difference is

4,

then it would be

2 n^{2},

you see,
but in this case the second difference is 3 ad when when

i

take the half of

3 (1.5)

does not work

how can

i

go about finding the nth term when the second difference is an odd number?

thanks for any help

HAL9000

21:48 Uhr, 24.11.2022

> when i take the half of 3(1.5) does not work

It's sad that you don't read the postings. I repeat:

f (n) = \frac{3 n^{2} + n + 12}{2}

RASTA aktiv_icon

00:39 Uhr, 25.11.2022

i

made a mistake.

i

forgot to change the value of

n

. I'll fix it and post my work tomorrow. Sorry.

RASTA aktiv_icon

01:46 Uhr, 25.11.2022

when

n = 1 (f 1) = 3 {(1)}^{2} + 1 + \frac{12}{2} = 8

when

n = 2 f (2) = 3 {(2)}^{2} + 2 + \frac{12}{2} = 13

and so forth and so on until,

n = 7 f (7) = 3 {(7)}^{2} + 7 + \frac{12}{2} = 83

Thanks,
Just one doubt . this is a set formula or you come up with it. I have not seen it in the videos

i

have watched

3 n^{2},

I know, but why

. .

+ n + \frac{12}{2}

the 2 diivides everytihng just in case it doesn;t show properly

I will appreciate your answer. thanks a lot for such a good support.

HAL9000

10:20 Uhr, 25.11.2022

A direct way to obtain the formula

f (n)

uses the first elements of each row of the iterated differences, i.e. "8 , 5 , 3":

f (n) = 8 + 5 \cdot (n - 1) + \frac{3}{2} \cdot (n - 1) (n - 2) = \frac{3 n^{2} + n + 12}{2}

See en.wikipedia.org/wiki/Newton_polynomial#Application for details.

RASTA aktiv_icon

15:48 Uhr, 25.11.2022

Super!. I get it.Das verstehe ich vollkommen!. thanks, Hal!

RASTA aktiv_icon

15:48 Uhr, 25.11.2022

Super!. I get it.Das verstehe ich vollkommen!. thanks, Hal!

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