There are two series A & B. In series A, each succeeding term is twice the preceding term. In series B, each succeeding term is three times the preceding term. If A₁ = 5 and B₁ = 2, then the minimum value of n for which A_n B_n is

Using the given rules, the terms of series A are 5, 10, 20, 40, 80 and the terms of series B are 2, 6, 18, 54. Checking the product of the terms, the product of the third terms is 20 multiplied by 18, which equals 360. The product of the fourth terms is 40 multiplied by 54, which equals 2160. Therefore, the minimum value of n for which the product An multiplied by Bn exceeds 1000 is 4.

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