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📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 5Question: What is the remainder when the sum of the sequence starting at $11071$ with a common difference of $2$ up to $5$ terms is divided by $8$?

📌 Solution: The sequence is $11071, 11073, 11075, 11077, 11079$. The sum of an arithmetic sequence is given by $S = \frac{n}{2}(a_1 + a_n)$. Here, $n = 5$, $a_1 = 11071$, and $a_5 = 11079$.

📌 S = \frac{5}{2}(11071 + 11079) = \frac{5}{2}(22150) = 5 \cdot 11075 = 55375

📌 Now compute $55375 \mod 8$. We divide $55375$ by $8$:

📌 \div 8 = 6921 \text{ remainder } 7

📌 Thus, the remainder is $\boxed{7}$.

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