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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,..........
Solution
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
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