Question

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

Answer 1

Answer: (B)

Common terms are $5,11,17,\dots$
$\therefore$ 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
$=3+(100-1)2=201$
$\Rightarrow t_n\le 201$
$\Rightarrow 6n-1\le 201$
$\Rightarrow n\le 33\frac{2}{3}$
$\therefore n=33(\because n\in N)$