Adding Consecutive Terms of Arbitrary Fibonacci Sequence, Method 1

This method for summing consecutive terms of an Arbitrary Fibonacci Sequence uses a telescoping series. The sum of the first $n$ terms of a sequence starting with $A_1, A_2, ...$ is given by the formula:

Sum = $A_{n+2} - A_2$

To use this, you must find the $(n+2)^{th}$ term in the sequence. For example, to sum the first 7 terms of 4, 7, 11, ..., you would need to calculate up to the 9th term ($A_9$). If $A_7=76$ and $A_8=123$, then $A_9=199$. The sum is $A_9 - A_2 = 199 - 7 = 192$. This method is best when most of the sequence is already provided in the problem.