Question
How many multiples of $4$ lie between $10$ and $250?$
✓
Answer
The multiples of 4 that lie between $10$ and $250$ are:
$12, 16, 20, 24, ...., 248$
$a_2 - a_1 = 16 - 12 = 4$
$a_3 - a_2 = 20 - 16 = 4$
$a_4 - a_3 = 24 - 20 = 4$
As $a_{k+1} - a_k$ is the same for $k = 1, 2, 3$, etc.
The above list of numbers forms an AP with the first term $a = 12$
and the common difference $d = 4$
Last term $(l) = 248$
Let there be n term s in this AP. Then, nth term = l
$ \Rightarrow a + (n - 1)d = 248$
$ \Rightarrow 12 + (n - 1)4 = 248$
$ \Rightarrow (n - 1)d = 248 - 12$
$ \Rightarrow (n - 1) = 236$
$ \Rightarrow n - 1 = \frac{{236}}{4}$
$ \Rightarrow n - 1 = 59$
$ \Rightarrow n = 59 + 1$
$ \Rightarrow n = 60$
Hence, 60 multiples of 4 lie between 10 and 250.
$12, 16, 20, 24, ...., 248$
$a_2 - a_1 = 16 - 12 = 4$
$a_3 - a_2 = 20 - 16 = 4$
$a_4 - a_3 = 24 - 20 = 4$
As $a_{k+1} - a_k$ is the same for $k = 1, 2, 3$, etc.
The above list of numbers forms an AP with the first term $a = 12$
and the common difference $d = 4$
Last term $(l) = 248$
Let there be n term s in this AP. Then, nth term = l
$ \Rightarrow a + (n - 1)d = 248$
$ \Rightarrow 12 + (n - 1)4 = 248$
$ \Rightarrow (n - 1)d = 248 - 12$
$ \Rightarrow (n - 1) = 236$
$ \Rightarrow n - 1 = \frac{{236}}{4}$
$ \Rightarrow n - 1 = 59$
$ \Rightarrow n = 59 + 1$
$ \Rightarrow n = 60$
Hence, 60 multiples of 4 lie between 10 and 250.
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