The number of terms between 11 and 200 which are divisible by 7 but not by 3 are :

Solution (By Examveda Team)

Multiples of 7 between 11 and 200 are 14, 21, 28, 35, 42, ..... , 189, 196
T_m = 196
⇒ 14 + (m - 1) × 7 = 196
⇒ (m - 1) × 7 = 182
⇒ (m - 1) = 26
⇒ m = 27
Multiples of 7 and 3 both, i.e., that of 21 are 21, 42, 63, ....., 189
T_n = 189
⇒ 21 + (n - 1) × 21 = 189
⇒ (n - 1) × 21 = 168
⇒ (n - 1) = 8
⇒ n = 9
∴ Required number of terms = (27 - 9) = 18