Which of the following are APs? If they form an A.P. find the common difference *d* and write three more terms `sqrt3, sqrt6, sqrt9, sqrt12 ...`

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#### Solution

√3, √6, √9, √12 ...

Here,

a_{2} - a_{1} = `sqrt6 - sqrt3 = sqrt3 × 2 -sqrt3 = sqrt3(sqrt2 - 1)`

a_{3} - a_{2} = `sqrt9 - sqrt6 = 3 - sqrt6 = sqrt3(sqrt3 - sqrt2)`

a_{4} - a_{3} = `sqrt12 - sqrt9 = 2sqrt3 - sqrt3 × 3 = sqrt3(2 - sqrt3)`

⇒ a_{n+1} - a_{n} is not the same every time.

Therefore, the given numbers are forming an A.P.

Concept: Arithmetic Progression

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