In an arithmetic sequence, consecutive terms have a constant common difference. This means: (second term - first term) = (third term - second term). Set up the equation: \((2x + 3) - x = (4x - 1) - (2x + 3)\). Simplify left side: \(2x + 3 - x = x + 3\). Simplify right side: \(4x - 1 - 2x - 3 = 2x - 4\). Equation: \(x + 3 = 2x - 4\). Solve: \(3 + 4 = 2x - x\), so \(7 = x\). Therefore, x = 7. Verification: If x = 7, the terms are 7, 2(7) + 3 = 17, and 4(7) - 1 = 27. Check differences: 17 - 7 = 10, and 27 - 17 = 10 ✓. Common difference is 10. This type of algebraic arithmetic sequence problem is very common in ECZ Paper 1. It tests both your understanding of the constant difference property and your algebra skills. The key insight is that for three consecutive terms a, b, c in an AP: b - a = c - b, which can be rearranged to 2b = a + c (the middle term is the average of the outer terms).

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Zambia

• Joseph Soko – 108 pts

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