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

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In NCERT how to solve the question of arithmetic progressions of exercise 5.2 of class 10th of math. How to solve this problem How many three digit numbers are divisible by 7?

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  1. First three-digit number that is divisible by 7 are;

    First number = 105

    Second number = 105+7 = 112

    Third number = 112+7 =119

    Therefore, 105, 112, 119, …

    All are three digit numbers are divisible by 7 and thus, all these are terms of an A.P. having first term as 105 and common difference as 7.

    As we know, the largest possible three-digit number is 999.

    When we divide 999 by 7, the remainder will be 5.

    Therefore, 999-5 = 994 is the maximum possible three-digit number that is divisible by 7.

    Now the series is as follows.

    105, 112, 119, …, 994

    Let 994 be the nth term of this A.P.

    first term, a = 105

    common difference, d = 7

    an = 994

    n = ?

    As we know,

    an = a+(n−1)d

    994 = 105+(n−1)7

    889 = (n−1)7

    (n−1) = 127

    n = 128

    Therefore, 128 three-digit numbers are divisible by 7.

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