This question is from NCERT Book class 10th Ch. no.5 Ex. 5.1 Q. 13 (xiii). In this question find that the given series is an A.P or not then find the common difference and the next three terms of the series. Give the solution of the question above given above.

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Solution:√3, √6, √9, √12 …

The difference between the above terms is:-

a_{2}–a_{1}= √6 – √3 = √3 × √2 – √3 = √3(√2 – 1)a_{3}–a_{2}= √9 – √6 = 3 – √6 = √3(√3 – √2)a_{4}–a_{3}= √12 – √9 = 2√3 – √3 × √3 = √3(2 – √3)The c.d is not same in each of the above cases.

So, the given series does not form a A.P.