Which of the following squences are A.P.? If they are A.P. find the common difference
3,`3 + sqrt(2) , 3 + 2sqrt2, 3 + 3sqrt3,` …

Answer

The given sequence is an A.P. The common difference `=d=sqrt2`.

Explanation

Here, the first term `t_(1)=3`,
`t_(2)=t_(1)=3+sqrt2-3=sqrt2`.
`t_(3)-t_(2)=3+2sqrt2-(3+sqrt2)=3+2sqrt2-3sqrt2=sqrt2`
`t_(4)-t_(3)=3+3sqrt2-(3+2sqrt2)=3+3sqrt2-3-2sqrt2=sqrt2.`
The difference between ant two consecutive terms is constant.