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nth teerm

what is the quadratic nth term in this sequence
1) 2,9,18,29,42
2) 4,16,36,64,100
3) 4,7,12,19,28
I will show you how to do the first one and you can use my method to other questions.

2 9 18 29 42
7 9 11 13 =1st Difference between the terms
2 2 2 =2nd Difference between terms

The nth term will be in this form ax^2+bx+c

You can use three simple rules to find the a,b and c

2a= 2nd Difference. This is the difference between numbers you get the second time. I have shown the above. ^
2a=2
a=1

3a+b= 1st Difference. This is the first difference you get. Use the difference between Term 1 and Term 2. I have shown the above. ^ In this case, 7.
You already know what a is from before.
3a+b=7
3(1)+b=7
3+b=7
b=7-3
b=4

a+b+c= The First Term. In this case, 2
You already know what a and b is from before.
a+b+c=2
1+4+c=2
5+c=2
c=2-5
c=-3

Now you have a,b and c.

So you can just sub the numbers into
ax^2+bx+c
(1)x^2+(4)x+(-3)
x^2+4x-3.

There, now do the other questions. If you still need help, ask again and I will see what I can do. :smile:

Spoiler

(edited 6 years ago)

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