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Question
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
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Solution
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}\]......
We have:
\[a = \sqrt{2}\]
\[d = 3\sqrt{2} - \sqrt{2} = 2\sqrt{2}\]
\[a_{18} = a + \left( 18 - 1 \right)d \left[ a_n = a + \left( n - 1 \right)d \right] \]
\[ = a + 17d\]
\[ = \sqrt{2} + 17\left( 2\sqrt{2} \right)\]
\[ = \sqrt{2} + 34\sqrt{2}\]
\[ = 35 \sqrt{2}\]
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