How many multiples of 4 lie between 10 and 250?
60
Step 1: Identify the first and last multiples of 4 in the given range.
Numbers strictly between 10 and 250.
The first multiple of 4 greater than 10 is:
\[12\]
The last multiple of 4 less than 250 is:
\[248\]
Step 2: Recognize this forms an AP of multiples of 4.
AP: \(12, 16, 20, 24, \ldots, 248\)
First term \(a = 12\), common difference \(d = 4\).
Step 3: Use the nth-term formula to find how many terms.
General term of AP:
\[a_n = a + (n - 1)d\]
Here, the nth term equals 248:
\[248 = 12 + (n - 1)4\]
Subtract 12:
\[236 = 4(n - 1)\]
Divide by 4:
\[59 = n - 1\]
So,
\[n = 60\]
Conclusion: There are 60 multiples of 4 between 10 and 250.