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How many multiples of 3 lie between 20 and 205?

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answer is C.

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Detailed Solution

The multiple of 3 lie which from 20 to 205,

21, 24, 27, 30 \dots \dots \dots . 204

It is Arithmetic Progressions.
Here,
First term of the series, a= 21
Common difference (d) of the series

d = 24 - 21

d = 27 - 24

d = 30 - 27

d = 3

Last term

a_{n}

= 204.
The nth term of A.P is,

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

\Rightarrow 204 = a + (n - 1) d

\Rightarrow 21 + (n - 1) \times 3 = 204

\Rightarrow 21 + 3 n - 3 = 204

\Rightarrow 3 n + 18 = 204

\Rightarrow 3 n = 204 - 18

\Rightarrow 3 n = 186

\Rightarrow n = \frac{186}{3}

\Rightarrow n = 62

So, total 62 multiples of 3 are in between 20 and 205.
Therefore, option 3 is correct.

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