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प्रश्न
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,..........
उत्तर
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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संबंधित प्रश्न
In an AP, if the common difference (d) = –4, and the seventh term (a7) is 4, then find the first term.
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If the nth term of a progression is (4n – 10) show that it is an AP. Find its
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The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is ______.
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a = `1/2`, d = `-1/6`
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The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.
