Question

How many whole numbers between 17 and 200 are divisible by 3

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Find :}}$

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• Whole numbers between 17 and 200 are divisible by 3

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let 'n' Numbers between 17 & 200 are divisible by 3

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$\underline{\bold{\texttt{We can create an AP on it :</p><p>}}}$

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18 , 21 , 24 _ _ _ _ _ _ _ 198

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$\underline{\bold{\texttt{We know that :}}}$

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$\red{\bold{a_n \: = \: a \: + \: (n - 1)d}}$

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• a = First term of the AP = 18

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• n = Number of term in the AP = n

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• d = Common difference = 3

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• $\rm a_n$ = Last term = 198

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$\underline{\bold{\texttt{Putting the above values,}}}$

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$\sf \longmapsto 198 = 18 + (n - 1)3$

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$\sf \longmapsto 198 = 18 + 3n - 3$

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$\sf \longmapsto 198 = 15 + 3n$

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$\sf \longmapsto 198 - 15 = 3n$

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$\sf \longmapsto 183 = 3n$

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$\sf \longmapsto n = \dfrac { 183 } { 3 }$

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$\bf \dashrightarrow n = 61$

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Hence there are 61 numbers between 17 & 200 which are divisible by 3

$\rule{200}5$