Question

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `3, 3 + sqrt(2), 3 + 2sqrt(2), 3 + 3sqrt(2)`,...

Answer 1

`3, 3 + sqrt(2), 3 + 2sqrt(2), 3 + 3sqrt(2)`,...
Here, first term (a) = 3
and d = `3 + sqrt(2) - 2 = sqrt(2)`
`3 + 2sqrt(2) - 3 - sqrt(2) = sqrt(2)`
`3 + 3sqrt(2) - 3 + 2sqrt(2) = sqrt(2)`
∵ Common difference is same
∵ It is an A.P.
and next three terms are
`3 + 4sqrt(2), 3 + 5sqrt(2), 3 + 6sqrt(2)`,...