How many natural numbers are there between 23 | vedclass

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Question

(D) The natural numbers between $23$ and $100$ that are divisible by $6$ form an arithmetic progression.The first number greater than $23$ divisible b

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(D) The natural numbers between $23$ and $100$ that are divisible by $6$ form an arithmetic progression.The first number greater than $23$ divisible by $6$ is $24$.The last number less than $100$ divisible by $6$ is $96$.Using the formula for the $n^{th}$ term of an arithmetic progression: $a_n = a + (n - 1)d$,where $a = 24$,$d = 6$,and $a_n = 96$.$96 = 24 + (n - 1)6$$96 - 24 = (n - 1)6$$72 = (n - 1)6$$n - 1 = 72 / 6 = 12$$n = 12 + 1 = 13$Therefore,there are $13$ such numbers.

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

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