#I beg ,i donno how to do this sequence question-the help would be much appreciated !
limber bramble
clear step by step explanations please 🙂
Write the number tiles for each of the patterns below, what do you notice?
frosty ibex
1,7,19 - quadratic sequence??
first change 6 then 8 diffrent between then both 2
im not sure
limber bramble
first change 6 then 8 diffrent between then both 2
yes very well
do you know how to find the formula for quadratic sequences
frosty ibex
i didnt realise there was a formulae - atleast not one i needed to know for gcse?
i know like n^2 + n+ c so likee
an^2 + bn + c
nova yoke
an^2 + bn + c
U could sub in the different values of n u have to get three eqns and then find a,b and c
frosty ibex
i found this online but i dont understand itt
frosty ibex
U could sub in the different values of n u have to get three eqns and then find ...
can you explain whats been shown above?
i dont understand the 3a + b part
for example
limber bramble
yes i was referring to the 2a, 3a + b stuff
frosty ibex
ohh okay
limber bramble
okay so the 2nd difference (in this 6) is always equal to some number 2a
the a is the same value as your a in an^2 + bn + c
frosty ibex
i seee
limber bramble
for your first difference (in this case 6 again) then it is equal to 3a + b
and then your first term (in this case 1) is equal to a + b + c
so u always have to find a and then b and then c
frosty ibex
okay slightly lost as how does it change from 2a to 3a?
limber bramble
i don’t know because i haven’t ever watched a proof for this
it just is this way
2a is for the second difference
3a + b is for your first difference
limber bramble
yes ofc
frosty ibex
oki doki ill give it a try - thanks!
limber bramble
np come back if u need any help
weak moth
i don’t know because i haven’t ever watched a proof for this
f(n) = an²+bn+c
f(1) = a(1)²+b(1)+c=a+b+c
f(2) = 4a+2b+c
f(3) = 9a+3b+c
f(2)-f(1) = (4-1)a + (3-2)b + (1-1)c = 3a+b
f(3)-f(2) = 5a+b
[f(3)-f(2)]-[f(2)-f(1)] = 5a+b - (3a+b) = 2a
In terms of T₁, T₂, T₃ this reads as
T₁ = a+b+c
T₂-T₁ = 3a+b (first difference)
(T₃-T₂)-(T₂-T₁) = 2a (second difference)
frosty ibex
oh ! thanks for that too - i dont fully understand this just yet - but yk practice makes perfect so ill go over the links and hopefully i will be better versed over this topic
appreciate all the help!
limber bramble
f(n) = an²+bn+c
f(1) = a(1)²+b(1)+c=a+b+c
f(2) = 4a+2b+c
f(3) = 9a+3b+c
f(2)-f(1...
this is so pretty ty wifibad ur awesome