A) 17
B) 33
C) 50
D) 147
Correct Answer: B
Solution :
Common terms are 5, 11, 17,... \[\therefore \] term of common sequence, \[{{t}_{n}}=5+(n-1)6=(6n-1)\] Also, 100th term of first sequence \[=2+(100-1)3=299\] and 100th term of the second sequence \[=3+(100-1)2=201\] \[\Rightarrow \] \[{{t}_{n}}\le 201\] \[\Rightarrow \] \[6n-1\le 201\] \[\Rightarrow \] \[n\le 33\frac{2}{3}\] \[\therefore \] \[n=33\] \[(\because \,n\in N)\]
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