Question 893471: What's the equation for the following sequence:
2, 5, 6, 11, 12, 19, 20?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
x| 1| 2| 3| 4| 5| 6| 7|
-|--|--|--|--|--|--|--|
y| 2| 5| 6|11|12|19|20|
(1,2), (2,5), (3,6), (4,11), (5,12), (6,19), (7,20)
Taking the points where x is odd:
We find the quadratic equation through
(1,2), (3,6), (5,12), (7,20)
by substituting three of those points in y = ax˛+bx+c
Similar we take the points where x is even and find the
quadratic equation through
(2,5), (4,11), (6,19) where x is even
We compare the two quadratic equations:
When x is odd the coefficient of x in the parentheses is 4, and
when x is even the coefficient of x in the parentheses is 6
The average of 4 and 6 is 5
4 = 5-1 and 6 = 5+1
So the coefficient of x is 5+(-1)x in either case
---
When x is odd, the constant term in the parentheses is 3, and
when x is even, the constant term in the parentheses is 4
The average of 3 and 4 is 7/2
3 = 7/2-1/2 and 4 = 7/2+1/2
the constant term in the parentheses is 7/2+1/2(-1)x in either case
So the general term is
which simplifies to
In sequence notation we replace y by an and x by n
Edwin
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