Question 772418: 41, 31, 23, 17, 11,______
what would be the next term?
Thanks,
Urvashi
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let the first term be term 0, the second be term 1, and so on.
Then create a set of ordered pairs, (0,41), (1,31), (2, 23), and so on.
Now that you have a set of five ordered pairs, you can find a fourth degree polynomial function that exactly fits the data.
The general 4th degree polynomial function is:
\ =\ ax^4\ +\ bx^3\ +\ cx^2\ +\ dx\ +\ e)
Since we know that \ =\ 41) , we can write:
\ =\ a(0)^4\ +\ b(0)^3\ +\ c(0)^2\ +\ d(0)\ +\ e\ =\ 41)
From which it is obvious that 
Then
\ =\ a(1)^4\ +\ b(1)^3\ +\ c(1)^2\ +\ d(1)\ +\ 41\ =\ 31)
From which we derive:
Similarly, you can derive three other linear equations in a, b, c, and d. I'll leave this as an exercise for the student.
You should now have the following 4 equations:
Solve the 4X4 system by any convenient means (I use the MDTERM function in Excel and Cramer's rule)
Once you have the four coefficients a, b, c, and d, write your function:
\ =\ ax^4\ +\ bx^3\ +\ cx^2\ +\ dx\ +\ 41)
By plugging in the values.
Finally, calcualate ) . Write back and let me know what you got. I'll let you know if you did it correctly.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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