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)`

a₄ = `4sqrt(3)`

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

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

a₄ – a₃ = `4sqrt(3) - 3sqrt(3)= 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,

`4sqrt(3) + sqrt(3), 4sqrt(3) + 2sqrt(3), 4sqrt(3) + 3sqrt(3)`

`5sqrt(3), 6sqrt(3), 7sqrt(3)`