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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?

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?

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
As we know
Total plants in original condition = 
= 1*1 + 2*2 + 3*3 + 4*4 +........n²
= 1² + 2² +3² + 4² +......+ n²
= n(n+1)(2n+1)/6
Now
As in a particular row plants has been doubled let assumed row is K th.
Hence..
(1² +2²+3³+4²+....+n²) + k² = 900
n(n+1)(2n+1)/6 + k² = 900
k² = 900 - n(n+1)(2n+1)/6
RHS should be a complete square because row is an integer.
This is satisfied only when n = 13
Now
k² = 900 - 819
k² = 81
k = 9
 
Hence that particular row is 9th row.
 
Regards
Arun (askIITians forum expert)

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