Immediate is wishful thinking! I think you mean 3, 12, 27, ...? We are doing 3n^2 so we started with n^2, which is the square numbers, 1, 4, 9, 16, 25 Then we multiply each of these by 3 giving 3, 12, 27, 48, 75
Why we use the 1,4,9,16,25 values to multiply with woth to get the answer 3,12,27,48,75...kindly anyone plz help me at this stage bcz I didn't get the point from where we get 1,4,9,16,25 values
Same way. The second difference is 2 so you have n^2. Subtract this (1,4,9,16,25) from the sequence and you get 3,5,7,9,11 The nth term of the linear part is 2n+1 so n^2 + 2n + 1
@@1stClassMathsoh wow you replied to soo many comments!! that mustve taken a long time ahah.. thank you so much for this video, its so helpful.. i was struggling to understand it in my class but this made it so much easier for me!!
Thank you so much, my school did a 1 hour lesson on this and they werent able to teach anyone. I sent this to everyone in my class, we are saved! Thank you so much, you're doing gods work
It helped a lot . Thanks ❤❤❤ I didn’t understand a thing about how to find the nth term of a quadratic sequence but after this video , you would think I was Einstein!! 😂😂 Thanks again😊😊
a+b+c = first original term 3a + b = 1st diff first term 2a = 2nd diff first term a+b+c = 8, 12, 20, 32, 48 3a+b = 4, 8, 12, 16 2a = 4, 4, 4 a = 2, b = -2 c = 8 2n^2 - 2n + 8
@@JoelPersson2003 this method oftens leads to a lack of understanding of what is going on. Those who just learn rules without knowing what they are doing or why often struggle with more difficult problems. In my experience of teaching this students much prefer the method I used in the video. Check the pinned comment...
Thank you so much! Also here's another method: a: second diff / 2 b: 3a+b = first diff of first term c: a+b+c = first term Now, all you have to do is sub a, b, and c into the equation T(n) = an²+bn+c. *Leave T and n as variables
This is a spectacular explanation. I am a middle school math teacher who has been struggling to grasp an easy way to explain this for weeks. Thanks so much!
The last example is 2nsqure+-3n+5 not 2nsqure-3n+5 ,you forget to put the plus, if you want to work out the first term of the original sequence by using 2nsqure-3n+5 it will be 2-2 which is 0 but if use 2nsqure+-3n+5 it will be 2+2 which 4, in all cases we adding because the third sequence plus the second sequence equal the first sequence
Hi. Unfortunately you are not correct here. 2n^2 + - 3n + 5 is equivalent to 2n^2 - 3n + 5 (which is the answer). When you add a negative it is just the same as subtracting. Your errors comes in your substitution. If you substitute in n = 1 you get 2*(1)^2 - 3(1) + 5 = 2 - 3 + 5 = 4
sometimes theres a sub question after you find the nth term of the sequence where it asks you to prove if a number is apart of the nth term of the sequence that you just found out. how do you do those sort of questions? (also thanks for explaining this topic so well it makes alot more sense now)
(second difference/2)×n² square numbers multiplied by 2 (including 1) subtract the original sequence by the square numbers multiplied by 2 find the general rule for the new linear sequence brought forth by subtracting the two (first difference×n + first term-x=first difference)
Hello, why doesn’t the quadratic sequence formula work here? I do an^2 + bn + c but i get incorrect answers while in other questions i use the formula and its correct
If you want a easier way to find b,the equation 3a + b=the first term of the first sequence.It will give you value of b,you can find the value of c using the quadratic equation,an2+bn+c,put the value of a and b and find c,btw the 2 in an2 represents the n being squared.
You taught this much better than my teacher, my teacher explained it differently, i did understand but your explanation is way better, thank you a lot im using you to revise for my end of year 9 assessment
sorry to ask, but how did you find a sequence for 3n^2 on the first one, do i just square root like the first one i have to square root, then the second one, then the third one?
Great question. This just means the nth term of it is simply the constant number. So if it's always 3, 3, 3, 3, your nth term might be something like n^2 + 3
You are the best, this video taught me more than any of my teachers have ever about this topic, I finally understand how to do these types of questions!!!!!, THANKYOU!!!!
Man thank you so much for this video you are a legend i have a assessment on this topic and it is worth half my grade aand i didnt understand a thing my teacher taught me vut after watching this video i understand so much that i might just ace the assignment thx so much
