In a garden there are 50 plants, planted in rows with the same number of plants in each row. The number of flowers on every plant of a row is the square of the row number. If the total number of flowers is 550, find the number of rows?
Explanation:
Let the number of rows be r and number of plants in each row be p.
∴ r × p = 50 …(1)
Number of flowers on a plant in nth row = n2 ∴ Total number of flowers in nth row is n2 × p.
Total number of flowers in the garden = p × (12 + 22 + 32 + … + r2) = 550
⇒ pr(r + 1)(2r + 1)/6 = 550
⇒ 50 × (r + 1)(2r + 1)/6 = 550 [from (1): rp = 50]
⇒ (r + 1)(2r + 1) = 66 = 6 × 11
⇒ k = 5.
Hence, 5.
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