Starting from the number $$1$$, Ritu generates a series of numbers as $$1,3,6,11,18,29,42,\ldots$$ such that the differences of the consecutive numbers from the beginning give consecutive primes. In this series she came across a perfect square for the first time. The square root of this perfect square is
Solution
Starting with $$1$$, add the consecutive primes $$2,3,5,7,11,\ldots$$. The terms obtained are $$1,3,6,11,18,29,42,59,78,101,130,161,198,239,282,329,382,441$$. The first new perfect square is $$441=21^2$$, so its square root is $$21$$.
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