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प्रश्न
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt3, sqrt6, sqrt9, sqrt12 ...`
उत्तर
`sqrt3, sqrt6, sqrt9, sqrt12`
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 do not form an AP.
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