SOLUTION: Find the sum of series 1+4+13+40+121 to n terms

Question 1000919: Find the sum of series 1+4+13+40+121 to n terms

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
to terms

The first thing you should always do is look at the differences between the terms:

....and so on.
terms: , , , , , ...
differences: , , ,
Now we can see a pattern in the differences: where =,,....and so on, because , , ,
So the next number must be

and the next one is

the th term can be calculated using the formula:

and the sum can be calculated using the formula:
+...+
To find the sum of the first n terms of an arithmetic series use the formula,

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