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.

juriemagic Oct 13, 2020

#1**+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)

ElectricPavlov Oct 13, 2020

#5**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**+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"]

Guest Oct 13, 2020

#4**+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.

Melody Oct 14, 2020

#6**+1 **

Melody!!!...,

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

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**+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