Question

Verify that the following is an AP, and then write its next three terms.

`sqrt(3), 2sqrt(3), 3sqrt(3),...`

Answer 1

Here,

a₁ = `sqrt(3)`

a₂ = `2sqrt(3)`

a₃ = `3sqrt(3)`

a₂ – a₁ = `2sqrt(3) - sqrt(3) = sqrt(3)`

a₃ – a₂ = `3sqrt(3) - 2sqrt(3)= sqrt(3)`

∵ a₂ – a₁ = a₃ – a₂ = `sqrt(3)`

Since, difference of successive terms are equal,

Hence, `sqrt(3), 2sqrt(3), 3sqrt(3),...` is an AP with common difference `sqrt(3)`

Therefore, the next three term will be,

a₄ = a₁ + 3d

= `sqrt(3) + 3(sqrt(3))`

= `4sqrt(3)`

a₅ = a₁ + 4d

= `sqrt(3) + 4sqrt(3)`

= `5sqrt(3)`

a₆ = a₁ + 5d

= `sqrt(3) + 5sqrt(3)`

= `6sqrt(3)`