Question

Show that the progression given below is an AP. Find the first term, common difference and next term.

`sqrt(2), sqrt(8), sqrt(18), sqrt(32)`,....

Answer 1

The given progression `sqrt(2), sqrt(8), sqrt(18), sqrt(32)`,....

This sequence can be written as `sqrt(2), 2sqrt(2), 3sqrt(2), 4sqrt(2)`,....

Clearly, `2sqrt(2) - sqrt(2) = 3sqrt(2) - 2sqrt(2)`

= `4sqrt(2) - 3sqrt(2)`

= `sqrt(2)`   ...(Constant)

Thus, each term differs from its preceding term by `sqrt(2)`. 

So, the given progression is an AP.

First term = `sqrt(2)`

Common difference = `sqrt(2)`

Next term of the AP =  `4sqrt(2) + sqrt(2)`

= `5sqrt(2)`

= `sqrt(50)`