SOLUTION: What is the formula for this pattern? 10, 9, 6, 1, -6 I understand that each number decreases by an odd number that is 2 more than the previous one, but I'm uncertain about ho

Algebra ->  Equations -> SOLUTION: What is the formula for this pattern? 10, 9, 6, 1, -6 I understand that each number decreases by an odd number that is 2 more than the previous one, but I'm uncertain about ho      Log On


   

Question 772029: What is the formula for this pattern?
10, 9, 6, 1, -6
I understand that each number decreases by an odd number that is 2 more than the previous one, but I'm uncertain about how to write that as an algebra formula. I came up with 2n-(n+1), but it only worked for the first one. If you could explain how you got an answer, that would also be very welcome.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Here is something you should find:

10-9=1
10-6=4
10-1=9
10-%28-6%29=16

Do you notice that the difference between each term and the FIRST term is a square? (the first term is 10)

Make a data table with column headings to identify index, the term, expression for difference from 10, and expression to show how that difference is composed.

You should see, for index n, each term is 10-%28n-1%29%5E2.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the formula for this pattern?
10, 9, 6, 1, -6
I understand that each number decreases by an odd number that is 2 more than the previous one, but I'm uncertain about how to write that as an algebra formula. I came up with 2n-(n+1), but it only worked for the first one. If you could explain how you got an answer, that would also be very welcome.

Formula, based on pattern: highlight_green%28a%5Bn%5D+=+a%5B1%5D+-+%28n+-+1%29%5E2%29, with:

"n" being the term number

a%5Bn%5D being term number n's value

a%5B1%5D being the 1st term, or 10

Using the above pattern rule, or formula, a%5Bn%5D+=+a%5B1%5D+-+%28n+-+1%29%5E2, term number 6, or a%5B6%5D+=+10+-+%286+-+1%29%5E2 ------ a%5B6%5D+=+10+-+5%5E2 ------ a%5B6%5D+=+10+-+25
highlight%28a%5B6%5D+=+-+15%29

You can check other terms' values using this formula!!

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