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  • Verify that each of the following is an AP, and then write its next three terms. root 3,2root 3, 3 root 3

Verify that each of the following is an AP, and then write its next three terms. root 3,2root 3, 3 root 3

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\text{Here the given series is } \sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, \ldots . \\ \text{Here, the common difference is the same. Hence, the given series is an AP.} \\ a_{4} = a_{1} + 3d \quad (\text{using } a_{n} = a_{1} + (n-1)d) \\ = \sqrt{3} + 3\sqrt{3} = 4\sqrt{3} \\ a_{5} = a_{1} + 4d \\ = \sqrt{3} + 4\sqrt{3} = 5\sqrt{3} \\ a_{6} = a_{1} + 5d \\ = \sqrt{3} + 5\sqrt{3} = 6\sqrt{3} \\ \text{Next terms are } 4\sqrt{3}, 5\sqrt{3}, 6\sqrt{3}.

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