Question

find the sum of all the numbers between 200 and 500 which are divisible by 7​

Answer 1

$\textbf{To find:}$

$\textsf{The sum of all the numbers between 200 and}$

$\textsf{500 which are divisible by 7}$

$\textbf{Solution:}$

$\textsf{The numbers which are divisible by 7 are}$

$\mathsf{203,214,.\;.\;.\;.\;497}$

$\textsf{This forms an A.P}$

$\mathsf{Here,\;a=203,\;d=7,\;l=497}$

$\boxed{\mathsf{n=\dfrac{l-a}{d}+1}}$

$\mathsf{n=\dfrac{497-203}{7}+1}$

$\mathsf{n=\dfrac{294}{7}+1}$

$\mathsf{n=42+1}$

$\implies\boxed{\mathsf{n=43}}$

$\mathsf{Required\;sum}$

$\mathsf{S_n=\dfrac{n}{2}[a+l]}$

$\mathsf{S_{43}=\dfrac{43}{2}[203+497]}$

$\mathsf{S_{43}=\dfrac{43}{2}{\times}700}$

$\mathsf{S_{43}=43{\times}350}$

$\implies\boxed{\mathsf{S_{43}=15050}}$

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Answer 2

Given :  numbers between 200 and 500

To Find  : Sum of all the numbers  which are divisible by 7​

Solution:

numbers between 200 and 500

200/7 = 28.57

1st number  = 29*7

500/7 = 71.4

=> last number = 7 * 71

Sum  of  

7*29  + 7 * 30  + +  + 7*71

= 7(29 + 30 + + + 71)

Total numbers = 71 - 29 + 1 =  43

= 7 (43/2)(29 + 71)

= 7 (43)(50)

= 15050

the sum of all the numbers between 200 and 500 which are divisible by 7​

= 15050

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