QJEEM20Ma384d: JEE Main 2020 Mathematics - Class 11 JEEM20Ma384d Solution: The number of terms common to the two A.P.'s 3, 7, 11, .....,…

First A.P. is 3, 7, 11, 15, 19, 23, ..... 407

d₁ = 4

Second A.P. is 2, 9, 16, 23, ..... 709

d₂ = 7

First common term = 23

Common difference of new A.P using the common terms of the two given A.P's is d = L.C.M. (4, 7) = 28

Last term $\le$ 407

$\Rightarrow$ 23 + (n – 1) (28) $\le$ 407

$\Rightarrow$ n $\le$ 14.7

$\therefore$ n = 14