Final answer:
To find the sum of the first 56 terms of an arithmetic sequence with first term 6 and 56th term 226, use the formula Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, the sum is 6496.
Step-by-step explanation:
To determine the sum of the first 56 terms in an arithmetic sequence, the formula for the sum of an arithmetic series, \(S_n = \frac{n}{2}(a + l)\), proves useful. Here, \(S_n\) represents the sum, \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term. Given that the first term \(a\) is 6 and the last term \(l\) is 226, applying these values to the formula yields:
\[ S_n = \frac{56}{2}(6 + 226) = 28 \times 232 = 6496. \]
Therefore, the sum of the first 56 terms in the arithmetic sequence is 6496. This formulaic approach efficiently calculates the cumulative sum by considering the number of terms, the first term, and the last term, providing a straightforward method for summing arithmetic series.