Question

Find the sum of all numbers divisible by 6 in between 100 to 400.

Answer 1

See the attached file

Answer 2

12450 is the sum of all numbers between 100 to 400 which is divisible by 6

Given:

Numbers from 100 to 400  

To find :  

Sum of all numbers from 100 to 400 divisible by 6

Solution :

First write the numbers which is divisible by 6 between 100 to 400

The series becomes 102,108,…..396

The series is like an arithmetic progression, where a = 102, d = 108 – 102 = 6

To find the number of terms from 102 to 396,  

By formula, $t_{n}=a+(n-1) d$

Where $t_{n}=396$

396= 102+(n-1)6

396- 102=(n-1)6

294= (n-1)6

(n-1) = 49

n = 50.

To find the sum of all numbers by formula,  

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$S_{50}=\frac{50}{2}[2(102)+(50-1) 6]$

$\begin{array}{l}{S_{50}=25[204+294]} \\ {S_{50}=25[498]} \\ {S_{50}=12450}\end{array}$