How Many Multiples of 4 Lie Between 10 and 250?

• We need numbers greater than 10 that are perfectly divisible by 4.
• Let's check: 10 is not divisible by 4. 11 is not. But 12 is ($4 \times 3 = 12$).
• So, the very first multiple in our AP series is 12.
• First term ($a$) = 12.

• We need a number less than 250 that is perfectly divisible by 4.
• If we divide 250 by 4, we get a remainder of 2.
• So, we subtract the remainder from 250: $250 - 2 = 248$.
• Let's check: $248 \div 4 = 62$ (Perfect division!).
• So, the absolute last multiple in our series is 248.
• Last term ($a_n$) = 248.

Our massive Arithmetic Progression series looks like this: 12, 16, 20, ......, 248.

• First term ($a$) = 12
• Common Difference ($d$) = 4
• Last term ($a_n$) = 248

The famous AP formula is: $a_n = a + (n - 1)d$

Let's plug in the numbers:

• $248 = 12 + (n - 1)4$
• $248 - 12 = 4(n - 1)$
• $236 = 4(n - 1)$
• $236 \div 4 = n - 1$
• $59 = n - 1$
• $n = 59 + 1$
• $n = 60$

There are exactly 60 multiples of 4 that lie between 10 and 250.