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`        There are rows of plants in a garden such that First row has one plant ,second has two plants that has three plants and so on. The total number of plants in the garden is 900 when plants in a particular row are added twice.what is the number of plants in that row which is added twice?`
2 years ago

Arun
23811 Points
```							Dear student As we knowTotal plants in original condition = = 1*1 + 2*2 + 3*3 + 4*4 +........n²= 1² + 2² +3² + 4² +......+ n²= n(n+1)(2n+1)/6NowAs in a particular row plants has been doubled let assumed row is K th.Hence..(1² +2²+3³+4²+....+n²) + k² = 900n(n+1)(2n+1)/6 + k² = 900k² = 900 - n(n+1)(2n+1)/6RHS should be a complete square because row is an integer.This is satisfied only when n = 13Nowk² = 900 - 819k² = 81k = 9 Hence that particular row is 9th row. RegardsArun (askIITians forum expert)
```
2 years ago
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• Mind Map
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