Question
How many three digit numbers are divisible by 7?
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Answer
The three digit numbers are 100, ..... 999, 105 is the first 3 digit number which is divisible by 7 when we divide 999 with 7 remainder is 5. So, 999 - 5 = 994 is the last three digits divisible by 7 so, the sequence is
105, ....., 994
First term (a) = 105
Last term (1) = 994
Common difference (d) = 7
Let there are n numbers in the sequence
an = 994
a + (n - 1)d = 994
a + (n - 1)d = 994
105 + (n - 1)7 = 994
(n - 1)7 = 889
$\text{n}-1=\frac{889}{7}=127$
n = 128
$\therefore$ There are 128 numbers between 105, 994 which are divisible by 7.
105, ....., 994
First term (a) = 105
Last term (1) = 994
Common difference (d) = 7
Let there are n numbers in the sequence
an = 994
a + (n - 1)d = 994
a + (n - 1)d = 994
105 + (n - 1)7 = 994
(n - 1)7 = 889
$\text{n}-1=\frac{889}{7}=127$
n = 128
$\therefore$ There are 128 numbers between 105, 994 which are divisible by 7.
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