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Question

How many two-digit natural numbers are divisible by 7?


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Solution

Step 1: Identify the given sequence as an arithmetic progression

The first two digit natural number divisible by 7 is 14

The last two digit natural number divisible by 7is 98

The sequence of numbers 14,21,28,.,98 which is divisible by 7 is an arithmetic progression with1st term 14 and common difference of 7

Step 2 : Finding the number of terms in an arithmetic progression

The nth term of an arithmetic progression is given as

an=a+(n-1)d

Here,an=98,a=14,d=7

98=14+(n-1)784=7n-77n=91n=13

Hence, the number of two digit natural numbers divisible by 7 is 13


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