Question

how many terms of two digits are divisible by 3

Answer 1

The first two digit number which is divisible by 3 is 12.
and the second one is 15.
Similarly,
12, 15, 18, ...

So,

$a = 12 \\ \\ a_{2} = 15 \\ \\ d = a_{2} - a_{1} \\ d = 15 - 12 \\ d = 3 \\ \\ \bf \: The \: Last \: two \: digit \: number \: which \: is \\ \bf \: divisible \: by \: 3 \: is \: 99 \\ So, \\ a_{n} = 99$

We know that,

$a_{n} = a + (n - 1) d$

Substituting the values we get,

$99 = 12 + (n - 1) 3 \\ \\ 99 = 12 + 3n - 3 \\ \\ 99 = 9 + 3n \\ \\ 3n = 99 - 9 \\ \\ 3n = 90 \\ \\ 3(n) = 3(30) \\ \\ \bf \: n = 30$

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