It forms an AP with 105 as the first term, and 7 is the common difference
If we divide 999 by 7, 5 will be the remainder
999 - 5 = 994 is the maximum possible three-digit number, which is divisible by 7
So the final sequence is 105, 112, 119, .... 994
the nth term of an AP = 994
a = 105
d = 7
aₙ = 994
We should find n
nth term of an A.P. is aₙ = a + (n - 1)d
994 = 105 + (n - 1)7
889 = (n - 1)7
n - 1 = 889/7
n - 1 = 127
n = 127 + 1
n = 128
Therefore, when asked How many three-digit numbers are divisible by 7? then the answer will be 128 three-digit numbers are divisible by 7.
Summary:
How many three-digit numbers are divisible by 7?
128 three-digit numbers are divisible by 7.
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