Numerical answer
In an arithmetic progression, the first term is 5 and the common difference is 3. If the sum of the first n terms is 390, find n.
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Answer: 15
Sum formula: Sₙ = n/2 × [2a + (n−1)d] = n/2 × [10 + 3(n−1)] = 390. So n(3n+7) = 780... solving directly: n/2×(10+3n−3) = 390 ⟹ n(3n+7) = 780. Testing n=15: 15×(45+7)=15×52=780. ✓ So n = 15.
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