Question

Show that each of the progressions given below is an AP. Find the first term, common  difference and next term of each.
(iv) 2, 8, 18, 32,..........

 

Answer 1

The given progression `sqrt(2)`, `sqrt(8)`, `sqrt(18)`, `sqrt(32)`,..........
This sequence can be written as `sqrt(2)` ,2  `sqrt(2)` ,3  `sqrt(2)` ,4 `sqrt(2)`,........
Clearly, 2 `sqrt(2)` - `sqrt(2)` =  3 `sqrt(2)` - 2 `sqrt(2)` = 4 `sqrt(2)` - 3 `sqrt(2)` = `sqrt(2)` (Constant)
Thus, each term differs from its preceding term by 2, So, the given progression is an AP.
First term =`sqrt(2)`
Common difference = `sqrt(2)`
Next tern of the AP =  4 `sqrt(2)`  + `sqrt(2)` =  5 `sqrt(2)` = 50