Question

How many multiples of 4lie between 10 to 250 also find their sum

Answer 1

We need to find the number of multiples of 4 between 10 and 250.

The list of numbers would be as follows:

12,16,20,24,28,32,36,40,........248.12,16,20,24,28,32,36,40,........248.

The above list is an arithmetic series/arithmetic progression where the first number is 12, the last number is 248 and the common difference between the numbers is 4.

The nth term in an arithmetic sequence = a + (n-1)*d where a is the first term, d is the common difference.

In the arithmetic series above, a =12, d = 4 and let us assume there are n terms and we need to find the value of n. We know that the value of the last term i.e. nth term is 248.

So, 248=12+(n−1)∗4

248=12+4n−4

248=4n+8

248–8=4n

240=4n

n=240/4=60n

Thus, 248 is the 60th term in the series and hence there are 60 terms in the series.

Therefore number of multiples of 4 between 10 and 250 is 60.

Answer 2

Step-by-step explanation:

We will use the AP:

AP= 12, 16, 20,......248

first term, a=12,

common difference, d=14

last term ,an= 248

an = a + (n-1) d

248 = 12 + (n-1)4

n - 1 = 236/4

n = 59 + 1 = 60

Sn = (n/2) + (a + an) = (60/2) + (12+248) = 7800

hence there are 60 multiples of 4 between 10 and 250. Their sum is 7800.