The sum of the first 14 terms of the given arithmetic series is 371, calculated using the formula for the sum of an arithmetic series. None of the given answer choices match this result, indicating a possible error in the question or options.
The question is asking to find the sum of the first 14 terms (S14) of an arithmetic series where the first four terms are -6, -1, 4, and 9. To find the 14th partial sum, we can use the formula for the sum of an arithmetic series which is Sn = ½ n (a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.
In this case, we already know the first term a1 (-6) and the number of terms n (14), but we need to find the 14th term a14. The common difference d in the series is 5 (since -1 - (-6) = 5). We can determine the 14th term using the formula a14 = a1 + (14 - 1) • d, which equals -6 + 13 • 5 = 59. Now we can calculate S14: S14 = ½ • 14 • (-6 + 59) = 7 • 53 = 371.
Therefore, the sum S14 for the arithmetic series is 371. None of the provided options (A, B, C, D) match this result, so there may be an error in the presentation of the question or the options given.