Question

Which of the following form an AP? Justify your answer.

`sqrt(3), sqrt(12), sqrt(27), sqrt(48)`

Answer 1

We have,

a₁ = `sqrt(3)`, a₂ = `sqrt(12)`, a₃ = `sqrt(27)` and a₄ = `sqrt(48)`

a₂ – a₁ = `sqrt(12) - sqrt(3)`

= `2sqrt(3) - sqrt(3)`

= `sqrt(3)`

a₃ – a₂ = `sqrt(27) - sqrt(12)`

= `3sqrt(3) - 2sqrt(3)`

= `sqrt(3)`

a₄ – a₃ = `sqrt(48) - sqrt(27)`

= `4sqrt(3) - 3sqrt(3)`

= `sqrt(3)`

Clearly, the difference of successive terms is same

Therefore given list of numbers from an AP.