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Question
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
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Solution
\[\text { We have: }\]
\[ 3\sqrt{2} - \sqrt{2} = 2\sqrt{2}\]
\[5\sqrt{2} - 3\sqrt{2} = 2\sqrt{2}\]
\[7\sqrt{2} - 5\sqrt{2} = 2\sqrt{2}\]
\[\text { Thus, the sequence is an A . P . with the common difference being } (2\sqrt{2}) . \]
\[\text { The next three terms are as follows } : \]
\[7\sqrt{2} + 2\sqrt{2} = 9\sqrt{2}\]
\[9\sqrt{2} + 2\sqrt{2} = 11\sqrt{2}\]
\[11\sqrt{2} + 2\sqrt{2} = 13\sqrt{2}\]
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