The numbers of terms between 11 and 200 which are divisible by 7 but not by 3 are -

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 = 196 - 14
⇒ (m - 1) × 7 = 182
⇒ (m - 1) = 182/7
⇒ (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 = 189 - 21
⇒ (n - 1) × 21 = 168
⇒ (n - 1) = 168/21
⇒ (n - 1) = 8
⇒ n = 9
∴ Required number of terms = 27 - 9
= 18.