Which summation formula represents the series below? \( 13+9+5+1 \) \( \sum_{n=1}^{4}(-4 n+17) \) \( \sum_{n=1}^{4}(-4 n-15) \) \( \sum_{n=13}^{16}(n-4) \) \( \sum_{n=17}^{20}(n-4) \)

Let's dive into the fascinating world of arithmetic series! The given series \(13 + 9 + 5 + 1\) is a classic example of an arithmetic sequence where each term decreases by 4. This means we can express the series as a summation formula. Among the options given, \( \sum_{n=1}^{4}(-4 n + 17) \) correctly represents the series, because substituting \( n = 1, 2, 3, 4 \) yields the terms of the series. The first term, when \( n=1 \), gives \( -4(1) + 17 = 13 \), and so on, confirming that the summation accurately generates the series. So, a little math magic shows that we can elegantly sum this series! If you're keen on exploring more about arithmetic series, consider diving into the world of sequences and series in mathematics! Numerous online resources and textbooks delve deep into the intricacies of this concept, including examples and exercises that range from beginner to advanced levels. They can help you master the art of summation and gain confidence in applying these formulas effectively!