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Home » Optifine 1.12..2: Game-Changing Upgrade That’s Totally Free (Update Below)! - ClickBalance

Optifine 1.12..2: Game-Changing Upgrade That’s Totally Free (Update Below)! - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Question: A sequence of five real numbers forms an arithmetic progression. The sum of the first and fifth terms is $14$, and the sum of the second and fourth terms is $10$. Find the third term.

📌 Let the five terms of the arithmetic progression be:

📌 a - 2d, \, a - d, \, a, \, a + d, \, a + 2d

📌 First term + Fifth term: $(a - 2d) + (a + 2d) = 2a = 14 \Rightarrow a = 7$

📌 Second term + Fourth term: $(a - d) + (a + d) = 2a = 10$

📌 But this contradicts $2a = 14$. So letâs double-check the assumption.

📌 Actually, the second and fourth terms: $(a - d) + (a + d) = 2a = 10 \Rightarrow a = 5$

📌 So from the first condition: first + fifth = $2a = 14 \Rightarrow a = 7$

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