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  4. The number of terms common to the two A.P's 3,7,11,.... ,407 and 2 ,9 ,1 6 ,709 is

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Q. The number of terms common to the two $A.P's 3,7,11,.... ,407$ and $2 ,9 ,1 6 ,709$ is _____________

JEE MainJEE Main 2020Sequences and Series

Solution:

Common term are : $23, 51, 79, ..... T_{n}$
$T_{n} \le 407\quad\Rightarrow \quad23 + \left(n - 1\right)28 \le 407$
$\Rightarrow n \le 14.71$
$n = 14$