How many three-digit numbers are divisible by 7?
Solution:
We have to find the number of three-digit numbers which are divisible by 7.
aₙ = a + (n - 1)d is the nth term of AP.
Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.
First three-digit number that is divisible by 7 = 105
Next number = 105 + 7 = 112
Therefore, the series becomes 105, 112, 119, ...
Thus, 105, 112, 119, ... is forming an A.P. having the first term as 105 and a common difference of 7.
When we divide 999 by 7, the remainder will be 5.
Clearly, 999 − 5 = 994 is the maximum possible three-digit number that is divisible by 7.
Hence the final sequence is as follows:
105, 112, 119, ..., 994
Let 994 be the nth term of this A.P.
a = 105
d = 7
aₙ = 994
n = ?
We know that the 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
There are 128 three-digit numbers that are divisible by 7
☛ Check: NCERT Solutions for Class 10 Maths Chapter 5
Video Solution:
How many three-digit numbers are divisible by 7?
NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 13
Summary:
The number of three-digit numbers divisible by 7 is 128.
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