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Home » The Surprising Chords Behind ‘Amazing Grace’ That’ll Move Your Heart Instantly - Groen Casting

The Surprising Chords Behind ‘Amazing Grace’ That’ll Move Your Heart Instantly - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \[\boxed{120}.\]

📌 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.

📌 Let the five terms be

📌 \[ a - 2d, \, a - d, \, a, \, a + d, \, a + 2d. \]

📌 The sum of the first and fifth terms is:

📌 \[ (a - 2d) + (a + 2d) = 2a = 20 \Rightarrow a = 10. \]

📌 The second term is \( a - d = 10 - d \), and the fourth term is \( a + d = 10 + d \). Their product is:

📌 \[ (10 - d)(10 + d) = 100 - d^2 = 48. \]

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