Question 382298: What is the general formula for the following series.
5,9,18,34,59,95
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the general formula for the following series.
5,9,18,34,59,95
----
a(1)-----5
a(2)-----a(1)+2^2 = 9
a(3)-----a(2)+3^2 = 18
a(4)-----a(3)+4^2 = 34
----
a(n) = a(n-1) + n^2
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Cheers,
Stan H.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! What is the general formula for the following series.
5,9,18,34,59,95
The other tutor gave a recursion formula for the sequence, not a general
formula.
Make a difference table by writing the numbers in the left-most column.
Then make the next column by subtracting each number from the one just
below it, and writing it directly to the right of the number subtracted.
Keep do this until all a column hass all its numbers the same.
5 4 5 2
9 9 7 2
18 16 9 2
34 25 11
59 36
95
Since we must make three columns after the first to get to a column
which has all the same number, we know that the general equation will
be of degree 3.
So we assume a general term of this form:
with  ,  ,  , 
Substituting 1, 2, 3, and 4 for n
Simplifying:
Simplify further, substituting , , ,
Put the constants on the right:
Can you solve that system? If not post again asking how:
Solution A= , B= , C= , D=
Therefore: becomes:
Edwin
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