How many multiples of 4 lie between 10 and 250? Class 9

How many multiples of 4 lie between 10 and 250? Class 9

Question 1.

How many multiples of 4 lie between 10 and 250? Class 9

(Hint: All multiples of 4 form an AP. Find the smallest and largest multiples of 4 between 10 and 250.)

Solution:

The multiples of 4 between 10 and 250 are 12,16, 20, ..., 248

∴ Smallest and largest multiples of 4 is 12 and 248, respectively.

The list of multiples is an AP with first term a = 12 and common ratio, d = 16 - 12 = 4

Let the number of multiples of this AP be n.

Then

t_n = 248

∴ a + (n - 1)d = 248

∴ 12 + (n - 1) (4) = 248

∴ 4(n - 1) = 248 - 12

∴ n - 1 = $\frac{236}{4}$

∴ n - 1 = 59

∴ n = 60

∴ There are 60 multiples of 4 lies between 10 and 250.