Quadratic sequence: sum of the elements between given two elements

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I've googled a lot but couldn't find any solution for my problem. Is there any formula for calculating the sum of the elements between given two elements of quadratic sequence? For example: I have a sequence 2, 7, 14, 23, 34, 47 ...

I want to calculate the sum of the elements between, let's say, 4th and 6th elements. Thanks in advance.