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Hi friends,

I realise I have been posting a bit today...I do apologise..lately the grade 12 papers are just way above my comprehension..I REALLY do not know what to do here..

 

They say the following is a QUADRATIC sequence:

3y ; 7 ; 15 ; 2y+1

 

Determine y

 

I am totally stumped!..please be so kind and educate me on this?..Thank you all greatly.

 Oct 13, 2020
 #1
avatar+27695 
+2

Compute the differences between the serial terms

 

3y          7           15            2y+1

      3y-7        -8          -2y+14                  then compute the differences between these serial terms ....they should all be equal

             3y+1        2y -22                        these two terms are equal

 

3y+1  = 2y-22

y = -23                                (If I did this correctly....I just did a quick lesson on Quad Sequences)  cheeky

 
 Oct 13, 2020
 #5
avatar+748 
0

ElectricPavlov..

 

gosh it really makes soo much sense now!!..I do however have a question but will post that with my response to Melody..please feel free to also comment...thanx a million!!!

 
juriemagic  Oct 14, 2020
 #2
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+1

y = - 23

a_n = -34 n^2 + 178 n - 213 (closed form)

 

Sequence    -69, 7, 15, -45, -173, -369, -633, -965, -1365, -1833, -2369, -2973, ...

 

First difference = 76, 8, -60, -128, -196.....etc.

 

2nd difference    = -68, - 68, - 68, -68.......etc. [This is why it is called "Quadratic Sequence"]

 
 Oct 13, 2020
 #4
avatar+111124 
+1

EP has given you a good answer, my answer is the same.

 

I am just going to give you a couple of examples first to help you understand

 

 

Now for you one.  And this is exactly the same as what EP did

 

 

I hope EP and I have helped you understand.    laugh

 
 Oct 14, 2020
 #6
avatar+748 
+1

Melody!!!...laugh,

 

I do understand everything you had shared with me....really I do..thank you also for helping..again...smiley.

 

I do however need to ask something....with quadratic sequences we have a 1st and 2nd difference, okay, I know the second difference is ALWAYS Arithmetic by nature...The 1st one however, is that aslo always Aritmetic or can that be of a geometric nature as well?

 
juriemagic  Oct 14, 2020
 #7
avatar+111124 
+1

If it is a quadratic sequence,

 

the sequence of first differences has to be an arithmetic sequence.

 

BECAUSE the second sequence of differences must all be the identical same number.

 
Melody  Oct 14, 2020
 #8
avatar+748 
+1

Melody,

mmm, yes, that makes all the sense in the world!...thank you..laugh

 
juriemagic  Oct 14, 2020

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