SOLUTION: i need to know the nth term for and how. thanks. 8,43,138,323,628,1083, 1718....

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Question 939169: i need to know the nth term for and how. thanks.
8,43,138,323,628,1083, 1718....
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20855)   (Show Source): You can put this solution on YOUR website!

first find differences between each two given terms and go until you get all differences equal
--------------------------------....
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-----------------------------------=> third differences same, means we have degree function
first term is and it can be written as
if we have third degree function to get first term if starts with we can write it as
so, general equation for nth term is:

where =,,,........

check:
if





if





if








Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!
Here's the way I did it.  Not with a difference table.

Let the nth term be an.

I noticed first that the last digits go 8,3,8,3,8,3,8.

Since the last digits differ by ±5, I noticed that if 
we subtract 3 from each one, the last digits of the new 
sequence will go 5,0,5,0,5,0 and therefore all be 
multiples of 5.

Let's subtract 3 from each, and we get a sequence
which has nth term  

5, 40, 135, 320, 625, 1080, 1715

Let's divide them by 5 and get a sequence with 
nth term 

1, 8, 27, 64, 125, 216, 343

Aha. that is the sequence of cubes which has
nth term .

So we have the equation 







Edwin
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