Question

How many multiples of 4 lie between 10 and 250?

Answer 1

First multiple of \(4\) that is greater than \(10\) is \(12\). Next will be \(16\).
Therefore, \(12, 16, 20, 24, ….\)
All these are divisible by \(4\) and thus, all these are terms of an A.P. with first term as \(12\) and common difference is \(4\).
When we divide \(250\) by \(4\), the remainder will be \(2\).
Therefore, \(250 − 2 = 248\) is divisible by \(4\).
The series is as follows.
\(12, 16, 20, 24, …, 248\)
Let \(248\) be the nth term of this A.P.
\(a = 12\)
\(d = 4\)
\(a_n = 248\)
\(a_n = a + (n-1)d\)
\(248 = 12 + (n-1)4\)
\(\frac {236}{4} = n-1\)
\(59 = n-1\)
\(n = 60\)

Therefore, there are \(60\) multiples of \(4\) between \(10\) and \(250\).