Question

The number of common terms between the sequence given by $1,4,7,\mathrm{10.....298}$ and $2,4,6,\mathrm{8..........300}$ is

• A. 49
• B. 50
• C. 48
• D. 100

Answer 1

The correct option is B 50

For the common ratio being the lowest common multiple of $3$ and $2$ and initial term $a=4$ we have a series,

$a=4$

$d=6$

Now, $a_n\ge 298$

$\Rightarrow a+(n-1)d\le 298$

$\Rightarrow 4+(n-1)d\le 298$

$\Rightarrow (n-1)\le 294$

$\Rightarrow (n-1)\le \frac{294}{6}$

$\Rightarrow n\le 49+1$

$\Rightarrow n\le 50$

So, $n=50$ are the number of common terms