[13] How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?

For Competitive Exams

How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?

Explanation:

Required numbers are 24, 30, 36, 42, ..., 96

This is an A.P. in which $ a $ = 24, $ d $ = 6 and $ l $ = 96

Let the number of terms in it be $ n $.

Then t_n = 96 $\Rightarrow$ $ a $ + $\left(n - 1\right)$d = 96

$\Rightarrow$ 24 + $\left( n - 1\right)$ x 6 = 96

$\Rightarrow$ $\left( n - 1\right)$ x 6 = 72

$\Rightarrow$ $\left( n - 1\right)$ = 12

$\Rightarrow n $ = 13

Required number of numbers = 13.

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