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प्रश्न
Show that the progression given below is an AP. Find the first term, common difference and next term.
`sqrt(20), sqrt(45), sqrt(80), sqrt(125)`,....
योग
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उत्तर
This given progression `sqrt(20), sqrt(45), sqrt(80), sqrt(125)`,....
This sequence can be re-written as `2sqrt(5), 3sqrt(5), 4sqrt(5), 5sqrt(5)`,....
Clearly, `3sqrt(5) - 2sqrt(5) = 4sqrt(5) - 3sqrt(5)`
= `5sqrt(5) - 4sqrt(5)`
= `sqrt(5)` ...(Constant)
Thus, each term differs from its preceding term by `sqrt(5)`.
So, the given progression is an AP.
First term = `2sqrt(5) = sqrt(20)`
Common difference = `sqrt(5)`
Next term of the AP = `5sqrt(5) + sqrt(5)`
= `6sqrt(5)`
= `sqrt(180)`
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