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There are 20 urns such that the first urn contains 5 balls, the second contains 10 balls and in general the $k^{th}$ urn contains $2k + 1$ balls more that that in $(k - 1)^{th}$ urn. Then what is the total number of balls in all the urns?

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  • $\begingroup$ What have you tried so far? $\endgroup$ Commented Mar 28, 2019 at 15:36
  • $\begingroup$ Not AP, nor GP and not HP either. I don't have any idea what to do. $\endgroup$ Commented Mar 28, 2019 at 15:38
  • $\begingroup$ The $n$-th term of the sequence is $n^2+n+2.$ $\endgroup$
    – little o
    Commented Mar 28, 2019 at 15:47
  • $\begingroup$ $a_n = 2n+1 + a_{n-1}$ - @Brian $\endgroup$ Commented Mar 28, 2019 at 15:48

1 Answer 1

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The $n$-th term of the sequence is $n^2+2n+2.$ Hence the total number of balls in the urns is $$\sum\limits_{n=1}^{20} (n^2+2n+2)=3330.$$

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  • $\begingroup$ I don't think so. The third term is 17. Since 10 +(2*3+1)=17. But your sequence says the 3rd term is 14. $\endgroup$ Commented Mar 28, 2019 at 15:52
  • $\begingroup$ Yeah I have made a mistake. Now I hope it's correct. $\endgroup$
    – little o
    Commented Mar 28, 2019 at 15:53
  • $\begingroup$ @Abhinash Dutta have you checked my edited solution now? $\endgroup$
    – little o
    Commented Mar 28, 2019 at 15:56
  • $\begingroup$ Wow. You did it. It is correct. What type of sequence is it by the way? And what logic did you use to solve it? $\endgroup$ Commented Mar 28, 2019 at 16:03
  • $\begingroup$ It's an increasing sequence which is unbounded above. $\endgroup$
    – little o
    Commented Mar 28, 2019 at 16:04

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