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Find the 100th Term of the Sequence: Sqrt3, 2sqrt3, 3sqrt3...... - ICSE Class 10 - Mathematics

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Question

Find the 100th term of the sequence:

`sqrt3, 2sqrt3, 3sqrt3......`

Solution

The given A.P is `sqrt3, 2sqrt3, 3sqrt3`

Now 

`2sqrt3 - sqrt3 = sqrt3`

`3sqrt3 - 2sqrt3 = sqrt3` etc

hence the given sequence is an A.P with first term `a = sqrt3` and common difference `d= sqrt3`.

The general term of an A.P is given by

`t_n = a + (n - 1)d`

`=> t_100 = sqrt3 + (100 - 1)xx  sqrt3 = sqrt3 + 996sqrt3 = 100sqrt3`

So the 100th term is `100sqrt3`

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Solution Find the 100th Term of the Sequence: Sqrt3, 2sqrt3, 3sqrt3...... Concept: Arithmetic Progression - Finding Their General Term.
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