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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
Bihar CECEBihar CECE 2013
Solution:
Common terms are $5,11,17, \ldots$
$\therefore $ term of common sequence,
$t_{n}=5+(n-1) 6=(6 n-1)$
Also, $100\,th$ term of first sequence
$=2+(100-1) 3=299$
and $100\,th$ term of the second sequence
$=3+(100-1) 2=201 $
$\Rightarrow t_{n} \leq 201$
$\Rightarrow 6 n-1 \leq 201$
$\Rightarrow n \leq 33 \frac{2}{3}$
$ \therefore n=33 \,\,\,(\because n \in N)$