Numerical answer
The sum of the first 10 terms of an arithmetic progression is 210, and the sum of its first 6 terms is 78. Find the common difference of the progression.
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Answer: 4
Let first term = a, common difference = d. S₁₀ = 10/2×(2a+9d) = 5(2a+9d) = 210 → 2a+9d = 42. S₆ = 6/2×(2a+5d) = 3(2a+5d) = 78 → 2a+5d = 26. Subtracting: 4d = 16 → d = 4. (Then a = 3.) Check: S₁₀ = 5(6+36) = 210 ✓, S₆ = 3(6+20) = 78 ✓.
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