Q. Number of identical terms in the sequence 2, 5, 8, 11,… upto 100 terms and 3, 5, 7, 9, 11,… upto 100 terms, are
A) 17
B) 33
C) 50
D) 147
Explanation
(b)
$\because\$ Common terms are 5, 11, 17, …
$T_{n} = 5 + (n - 1)6$
$= 6n - 1$
100th term of the first sequence
$= 2 + (100 - 1)3 = 299$
and 100th term of the second sequence
$= 3 + (100 - 1)2 = 201$
Now, $201 > 6 - 1$
$\Rightarrow n \leq 33\frac{2}{3}$
$\Rightarrow n = 33\ \ \ \ \ \ \ \ (\because n \in N)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.