How many two-digit numbers are divisible by 3 | vedclass

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(A) The list of two-digit numbers divisible by $3$ is $12, 15, 18, \ldots, 99$.This sequence forms an Arithmetic Progression $(AP)$ where the first te

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) The list of two-digit numbers divisible by $3$ is $12, 15, 18, \ldots, 99$.This sequence forms an Arithmetic Progression $(AP)$ where the first term $a = 12$,the common difference $d = 3$,and the last term $a_n = 99$.The formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n - 1)d$.Substituting the values: $99 = 12 + (n - 1) 	imes 3$.Subtracting $12$ from both sides: $87 = (n - 1) 	imes 3$.Dividing by $3$: $n - 1 = 29$.Therefore,$n = 29 + 1 = 30$.Thus,there are $30$ two-digit numbers divisible by $3$.

How many two-digit numbers are divisible by $3$?

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