How many numbers are there between 11 and 90 which are divisible by 7?

Explanation

Numbers between 11 and 90 that are divisible by 7 are respectively: 14, 21, 28, ... 84 The series of these numbers is an arithmetic progression. $\therefore$ First term (a) = 14, d = 7 T$_n$ (n$^{th}$ term) = 84 T$_n$ = a + (n – 1) d 84 = 14 + (n – 1) 7 7 (n – 1) = 84 – 14 n – 1 = $\frac{70}{7} \Rightarrow 10$ $\therefore n = 10 + 1 \Rightarrow 11$