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Home » A sequence of five real numbers forms an arithmetic progression. The sum of the first and fifth terms is 20, and the product of the second and fourth terms is 48. Find the third term. - AMAZONAWS

A sequence of five real numbers forms an arithmetic progression. The sum of the first and fifth terms is 20, and the product of the second and fourth terms is 48. Find the third term. - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
A sequence of five real numbers forms an arithmetic progression. The sum of the first and fifth terms is 20, and the product of the second and fourth terms is 48. Find the third term.

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📌 Solution: The first 12 even numbers after 2020 are $2022, 2024, \ldots, 2044$. The sum of an arithmetic sequence is $S = rac{n}{2}(a_1 + a_n)$. Here, $n = 12$, $a_1 = 2022$, $a_n = 2044$. Thus, $S = rac{12}{2}(2022 + 2044) = 6 imes 4066 = 24396$. Dividing 24396 by 11: $11 imes 2216 = 24376$, so the remainder is $24396 - 24376 = 20$. However, $20 \mod 11 = 9$. Therefore, the remainder is $oxed{9}$.
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