Question

Number of identical terms in the sequence $2,5,8,\mathrm{11....}$ upto $100$ terms are

• A. $17$
• B. $33$
• C. $50$
• D. $147$

Answer 1

Answer: (B)

$33$

First sequence is $2,5,8,11,.....$ upto $100$ terms

Here, $n^{th}$ term is $2+(n-1)3$

Alternate terms are $5,11,17,.....$
$\therefore$ term of common sequence,
$t_n=5+(n-1)6=(6n-1)$
Also, 100th term of the first sequence
$=2+(100-1)3=201$
$\Rightarrow t_n\le 201$
$\Rightarrow 6n-1\le 201$

$\Rightarrow 6n\le 202$
$\Rightarrow n\le 33\frac{2}{3}$
$\therefore n=33$ $(\because n\in N)$