Question

How many2 digit numbers
are
by 3.​

Answer 1

Correct Question:

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

Answer:

There are 30 two-digit natural numbers divisible by 3.

Step-by-step explanation:

The two-digit natural numbers which are divisible by 3 are 12, 15, 18,......, 99.

Here,

$\bullet\sf\:a\:=\:12\\\\\\\bullet\sf\:t_n\:=\:99$

Now,

$\pink{\sf\:t_n\:=\:a\:+\:(\:n\:-\:1\:)\:d}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:99\:=\:12\:+\:(\:n\:-\:1\:)\:\times\:3\\\\\\\implies\sf\:(\:n\:-\:1\:)\:\times\:3\:=\:99\:-\:12\\\\\\\implies\sf\:(\:n\:-\:1\:)\:\times\:3\:=\:87\\\\\\\implies\sf\:n\:-\:1\:=\:\cancel{\dfrac{87}{3}}\\\\\\\implies\sf\:n\:-\:1\:=\:29\\\\\\\implies\sf\:n\:=\:29\:+\:1\\\\\\\implies\boxed{\red{\sf\:n\:=\:30}}$

There are 30 two-digit natural numbers divisible by 3.

Additional Information:

1. Arithmetic Progression:

1. In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).

2. $\sf\:n^{th}$ term of an AP:

The number of a term in the given AP is called as $\sf\:n^{th}$ term of an AP.

3. Formula for $\sf\:n^{th}$ term of an AP:

$\large{\boxed{\red{\sf\:t_{n}\:=\:a\:+\:(\:n\:-\:1\:)\:d}}}$

4. The sum of the first n terms of an AP:

The addition of either all the terms of a particular terms is called as sum of first n terms of AP.

5. Formula for sum of the first n terms of A. P. :

$\large{\boxed{\red{\sf\:S_{n}\:=\:\frac{n}{2}\:[\:2a\:+\:(\:n\:-\:1\:)\:d\:]}}}$

6. Trick to use the correct formula in the questions related to A.P.:

1. Use the formula for the $\sf\:n^{th}$ term of an AP where 'How many', 'Which term', 'Find first term or common difference' such words are used.

2. Use the formula for the sum of first n terms of AP where 'Sum', 'Total earning', 'Total number' such words are used.