Final answer:
The question involves calculating the sum of an alternating arithmetic sequence over 91 terms using a conditional approach.
Step-by-step explanation:
The student's question concerns the pattern and sum of the first 91 terms of a sequence. The given sequence, 2, -5, 8, -11, 14, ..., is arithmetic, where each term after the first is obtained by adding a constant difference, which alternates between +3 and -7.
To calculate the sum of the first 91 terms, we employ a conditional inside our loop to add or subtract terms based on whether the term number is odd or even. This method considers the pattern of addition and subtraction inherent in the sequence.
The sequence given can be represented as follows:
Term: 1 2 3 4 5 ...
Value: 2 -5 8 -11 14 ...
From the given sequence, we can observe that the sign of the number alternates between positive and negative, and the value increases by 3 with each subsequent term. This can be written as the expression 2n + (-1)^(n+1)*3, where n is the term number starting from 1. For example, for the 4th term, n=4, so the value is 2*4 + (-1)^(4+1)*3 = 8 - 3 = 5.