Question

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13. How many three-digit numbers are divisible by 7?​

Answer 1

Explanation:

The first three digit number which is divisible by 7 is 105 and last three digit number which is divisible by 7 is 994.

This is an A.P. in which a = 105, d = 7 and l = 994.

Let the number of terms be n . Then tn = 994.

nth term of A.P = tn = a + (n - 1)d.

⇒ 994 = 105 + (n -1)7.

⇒ 889 = 7(n-1)

⇒ n -1 = 127

∴ n = 128.

∴ There are128 three digit numbers which are divisible by 7.

Answer 2

Answer:

128

Explanation:

Simple rule of A.P

a= first three digit number divisible by 7

n= number of digit divisible by 7

d= the differences between the digits

an= the last three digit number divisible by 7

a=105

n=?

d=7

an =994

an= a+(n-1) *d

999= 105+(n-1)*7

994-105 =(n-1)*7

889=(n-1)*7

889/7=(n-1)

127 =n-1

n=127+1

n=128