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Question
Find the 100th term of the sequence:
`sqrt(3), 2sqrt(3), 3sqrt(3),..........`
Solution
The given A.P is `sqrt(3), 2sqrt(3), 3sqrt(3),..........`
Now,
`2sqrt(3) - sqrt(3) = sqrt(3)`
`3sqrt(3) - 2sqrt(3) = sqrt(3)`, etc.
Hence, the given sequence is an A.P. with first term `a = sqrt(3)` and common difference `d = sqrt(3)`.
The general term of an A.P. is given by
tn = a + (n – 1)d
`=> t_100 = sqrt(3) + (100 - 1) xx sqrt(3)`
= `sqrt(3) + 99sqrt(3)`
= `100sqrt(3)`
So, the 100th term is `100sqrt(3)`.
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