athomedad Posts: 1, Reputation: 1 New Member #1 Mar 4, 2008, 07:24 PM
how do you write the equation for this sequence 10, 12, 16, 22, 30
Hi, How do you write an equation for this sequence whose difference increases by two each time?
10, 12, 16, 22, 30
 galactus Posts: 2,271, Reputation: 282 Ultra Member #2 Mar 5, 2008, 07:03 AM
You can set up a system of equations using what is known as finite differences.

You have the numbers 10,12,16,22,30

If you subtract each consecutive entry you get 2,4,6,8

Subtract those and we get it down to 2,2,2.

Using the top row and $ax^{2}+bx+c$

Enter x=1 and we get a+b+c=10

Enter x=2 and get 4a+2b+c=12

Enter x=3 and get 9a+3b+c=16

Now you have a system of equations to solve for a,b,c

Those will be the coefficients of your quadratic. I will let you finish.

Let me know what you get.

After you have the equation you should be able to enter x=1 and get 10, x=4 and get 22 and so forth.
 jojokittty888 Posts: 1, Reputation: 1 New Member #3 Dec 6, 2010, 10:34 AM
2n+8 when used as a function so..
f(n)=2n+8
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #4 Dec 6, 2010, 11:16 AM
Originally Posted by jojokittty888
2n+8 when used as a function so..
f(n)=2n+8
No, this might work for the first and second terms, but doesn't work for the other terms onwards. This is a sequence which requires a quadratic function like galactus showed.

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