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