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Mathematics

The next two terms of the A.P., 3,12,27,......\sqrt{3}, \sqrt{12}, \sqrt{27}, …… are :

  1. 9 and 939\sqrt{3}

  2. 63 and 736\sqrt{3} \text{ and } 7\sqrt{3}

  3. 48 and 75\sqrt{48}\text{ and } \sqrt{75}

  4. 75 and 108\sqrt{75}\text{ and } \sqrt{108}

AP GP

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Answer

Given,

A.P. = 3,12,27,......\sqrt{3}, \sqrt{12}, \sqrt{27}, ……

The above A.P. can be written as

3,23,33,........\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, ……..

Above is an A.P. with first term (a) = 3\sqrt{3} and common difference (d) = 3\sqrt{3}

So, next two terms of A.P. are

33+3=43=42×3=483\sqrt{3} + \sqrt{3} = 4\sqrt{3} = \sqrt{4^2 \times 3} = \sqrt{48}.

43+3=53=52×3=754\sqrt{3} + \sqrt{3} = 5\sqrt{3} = \sqrt{5^2 \times 3} = \sqrt{75}.

Hence, Option 3 is the correct option.

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