# 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 ... - Mathematics

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 ...

#### Solution

√3, √6, √9, √12 ...

Here,

a2 - a1 = sqrt6 - sqrt3 = sqrt3 × 2 -sqrt3 = sqrt3(sqrt2 - 1)

a3 - a2 = sqrt9 - sqrt6 = 3 - sqrt6 = sqrt3(sqrt3 - sqrt2)

a4 - a3 = sqrt12 - sqrt9 = 2sqrt3 - sqrt3 × 3 = sqrt3(2 - sqrt3)

⇒ an+1 - an is not the same every time.

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

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.1 | Q 4.13 | Page 100