How many three-digit numbers are divisible by 7?

Explanation

All 3-digit numbers divisible by 7 are
105, 112, 119,…., 994.
Clearly, these numbers form an AP with
a = 105, d = (112-105) = 7 and l = 994.
Let it contain n terms. Then,
`T_(n) = 994 rArr a + (n-1) xx d = 994`
`rArr 105 + (n-1) xx 7 = 994`
`rArr 98 + 7n = 994 rArr 7n = 896 rArr n = 128.`
Hence, there are 128 three-digit numbers divisible by 7.`