Haryana Police Constable Model Paper 2

3 digits numbers divisible by 7 are: 105, 112, 119, ……, 994
This is an arithmetic progression series in which first term, a = 105, difference, d = 7 and last term Tn = 994
⇒ ${\mathrm{T}}_{\mathrm{n}}$ = a + (n – 1) × d
⇒ 994 = 105 + (n – 1) × 7
⇒ (n – 1) × 7 = 889
⇒ n – 1 = 127
∴ n = 128 three digits numbers are divisible by 7