Question

Which of the following sequences are A.P.? If they are A.P. find the common difference.

`3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2, ...`

Answer 1

t₂ − t₁ = `3 + sqrt2 - 3 = sqrt2`

t₃ − t₂ = `3 + 2sqrt2 - (3 + sqrt2)`

= `3 + 2sqrt2 - 3 - sqrt2`

= `sqrt2`

t₄ − t₃ = `3 + 3sqrt2 - (3 + 2sqrt2)`

= `3 + 3sqrt2 - 3 - 2sqrt2`

= `sqrt2`

∵ The difference between consecutive terms are same.

∴ Given sequence is an A.P.

Common difference (d) = `sqrt2`