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

ConceptArithmetic Progression - Finding Their General Term

#### 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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#### APPEARS IN

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