A) 9998
B) 9999
C) 10000
D) 100000
Correct Answer: A
Solution :
Let \[S=2+7+14+23+34+.....+{{T}_{n}}\] ?..(i) and \[S=\,\,\,\,\,\,\,\,\,\,2+7+14+.................+{{T}_{n-1}}+{{T}_{n}}\] ?..(ii) From (i) and (ii), we get \[0=2+[5+7+9+11........+{{T}_{n}}-{{T}_{n-1}}]-{{T}_{n}}\] \[\Rightarrow \] \[{{T}_{n}}=2+\left[ \frac{n-1}{2}\{2\times 5+(n-2)\,2\} \right]\] \[\Rightarrow \]\[{{T}_{n}}=2+(n-1)(n+3)\] Now put \[n=99\] \[\Rightarrow \]\[{{T}_{99}}=2+98\times 102=9998\].
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