Question

Find the sum of all numbers between 100 and 1000 which are divisible by 11

Answer 1

See the attach file for ur ans

Answer 2

44550 is the sum of all numbers between 100 and 1000 which are divisible by 11.

Given:

Numbers between 100 and 1000

To find:

Sum of all number between 100 and 1000 which are divisible by 11.

Solution:

The first number after 100 that is divisible by 11 is 111; therefore, the first number in the series is 111.

The last number or the number before 1000 that is a multiple of 11 is 999

Hence to find the sum of all the numbers that are divisible by 11 we are going to use the Sum of Arithmetic Progression method, but first let us find the number of such terms that are divisible by 11

$\begin{array}{l}{T_{n}=a+(n-1) d} \\ {999=111+(n-1) 11} \\ {\frac{888}{11}=(n-1)} \\ {\frac{888}{11}+1=n, \quad n=81}\end{array}$

Therefore, the sum of the numbers between 100 and 1000 is  

$\begin{array}{l}{S_{n}=\frac{n}{2}(2 a+(n-1) d)} \\ {S_{n}=\frac{81}{2}(550 \times 2)=44550}\end{array}$

Therefore, the sum of the numbers is equivalent to 44550.