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Given the sum of squares of the first 10 natural numbers equals 385, find the sum of squares of the sequence 3, 6, 9, ..., 30.
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Solution: Step 1: Identify the pattern: sequence is 3n where n = 1 to 10. Step 2: Sum of squares formula for first n natural numbers: Σn^2 = n(n+1)(2n+1)/6. Step 3: Verify given: Σ1^2 to Σ10^2 = 385 (matches formula). Step 4: Calculate sum of (3n)^2 = 9Σn^2 for n=1 to 10. Step 5: Apply formula: 9 * [10*11*21/6] = 9 * 385 = 3465. Final Answer: 3465
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