A) 300
B) 310
C) \[311\frac{2}{3}\]
D) \[333\frac{1}{3}\]
Correct Answer: B
Solution :
[b] The given series is arithmetic whose first term = 20, and common difference \[=-\frac{2}{3}\] As the common difference is negative the terms will become negative after some stage. So the sum is maximum when all positive terms are added Now, for the positive terms \[{{x}_{n}}\ge 0\Rightarrow 20+(n-1)\times -\frac{2}{3}\ge 0\] \[\Rightarrow \,\,\,60-2(n-1)\ge 0\Rightarrow n\le 31.\] \[\therefore \] The first 31 terms are non- negative \[\therefore \] Maximum sum \[={{S}_{31}}=\frac{31}{2}\left[ 2\times 20+(31-1)\times -\frac{2}{3} \right]=310\]
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