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celie of the color purple - Decision Point

📅 May 2, 2026 👤 scraface

May 02, 2026

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A sequence of five real numbers forms an arithmetic progression. The s...
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 +...
\[ (10 - d)(10 + d) = 100 - d^2 = 48. \]
Solve for \( d^2 \):
\[ 100 - d^2 = 48 \Rightarrow d^2 = 52. \]
But we are asked for the third term, which is \( a = 10 \).

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