The probability for Arts Club is 11 / 40 = 0.275 (27.5%). The sample proportion for Sports Club is 9 / 40. Across 800 students, the estimated count is (9 / 40) x 800 = 180 students.
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For green sweets, probability is 8 / 30 = 4 / 15 (or approximately 0.267). For yellow sweets, sample probability is 7 / 30. In 600 sweets, the expected yellow sweets count is (7 / 30) x 600 = 140.
Calculating values gives 1, 2, 3, 5, 8, 13, 21, 34. Subtracting consecutive terms reveals Wn – Wn-1 = Wn-2, which means Wn = Wn-1 + Wn-2. This is the Virahanka-Fibonacci sequence.
Computing terms yields 1, 2, 4, 8, 16, 32, 64, 128. Since Pn – Pn-1 = Pn-1, the simpler recursive rule is Pn = 2Pn-1 for n >= 3. The explicit formula is Pn = 2ⁿ⁻¹ for n >= 2 ...
Using a(1 + r + r²) = 26 and a²(1 + r² + r⁴) = 364, dividing squares gives (1 + r + r²) / (1 – r + r²) = 13/7, leading to r = 3 or 1/3. The ...