Solution: Substitute $ m + n = 8 $ into the first equation: $ m \cdot 8 = 24 $, so $ m = 3 $. oxed{3}Question: A sequence of six real numbers forms an arithmetic progression. The sum of the first three terms is 12, and the sum of the last three terms is 30. What is the sum of all six terms?

February 22, 2026

$Solution: Substitute $ m + n = 8 $ into the first equation: $ m \cdot 8 = 24 $, so $ m = 3 $. oxed{3}Question: A sequence of six real numbers forms an arithmetic progression. The sum of the first three terms is 12, and the sum of the last three terms is 30. What is the sum of all six terms?$

Question: Find the intersection of the lines $ y = 3x + 1 $ and $ y = -2x + 11 $.
Solution: Set $ 3x + 1 = -2x + 11 $. Solve for $ x $: $ 5x = 10 $ â $ x = 2 $. Substitute into $ y = 3(2) + 1 = 7 $. The intersection is $ (2, 7) $. oxed{(2, 7)}
Question: If $ m(m + n) = 24 $ and $ m + n = 8 $, what is the value of $ m $?
Solution: Let the six terms of the arithmetic progression be $ a - 2d, a - d, a, a + d, a + 2d, a + 3d $.
The sum of the first three terms is:
The sum of the last three terms is:

Solution: Substitute \( m + n = 8 \) into the first equation: \( m \cdot 8 = 24 \), so \( m = 3 \). oxed{3}Question: A sequence of six real numbers forms an arithmetic progression. The sum of the first three terms is 12, and the sum of the last three terms is 30. What is the sum of all six terms?

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