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How many multiples of 4 lie between 10 and 205?

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#### Solution

We need to find the number of multiples of 4 between 10 and 205.

So, multiples of 4 give the sequence 12, 16, ..., 204

a = 12, d = 4 and an=204">a_{n }= 204

Using the formula an=a+n-1d">a_{n }= a + (n−1)d

Plugging values in the formula we get

204=12+n-14204=12+4n-44n=196n=49">204 = 12 + (n−1)4

204 = 12 + 4n − 4

4n = 196

n = 49

Thus, there are 49 multiples of 4 between 10 and 205.

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