Consider the sequence 1,3, 3, 3, 5, 5,5, 5,5, 7,7, 7,7, 7,7,7,.... and evaluate its `2016^(th)` term.

Explanation

Let he terms of the sequences `a_1​,a_2​,...,a_(2016​),...`

Notice that the last term with value 1 is `a_1`​, the last term with the value 3 is `a_4`​, the last term with the value 5 is `a_9`​, and in general the last term with the value 2k−1 is `a_(Sk)​`​ where


`Sk​=1+3+5+7+.....+(2k−1)`

Then, to know the values of the terms in the subsequence containing `a_(2016)`​, we need only find k such that `S_(k−1)​ < 2016 <=S_k​`.
Then we will have `a_(2016)​=2k−1`

so,`S_k​=sum_(i=1)^k ​(2i−1)`


=`−k+2sum_(i=1)^k i`

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