Question

find the sum of all the numbers between 100 and 200 which are divisible by 7

Answer 1

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Answer 2

So, The sum of all the numbers between $100$ and $200$ which are divisible by $7$ is    $2107$

Step-by-step explanation:

Given;

Find the sum of all the numbers between $100$ and $200$ which are divisible by $7$

The smallest number in between $100$ and $200$ which is divide by $7$$=105$ and

The largest number in between $100$ and $200$ which is divide by $7$$=196$

Here,

smallest number$(a)=105$

largest number $(a_{n}=196$

All no divide by $(d)=7$

We know,

$a_{n}=a+(n-1)d$

Plug all value in above equation;

⇒$196=105+(n-1)7$

⇒$7n-7=196-105$

⇒$7n=91+7$

⇒$n=\frac{98}{7}$

∴$n=14$

∴The sum of all the numbers between $100$ and $200$ which are divisible by $7$ is equal to,

$s_{14} =\frac{n}{2}(a+a_{n})$

⇒$s_{14} =\frac{14}{2}(105+196)$

⇒$s_{14} =7\times 301$

∴$s_{14} =2107$

∴The sum of all the numbers between $100$ and $200$ which are divisible by $7$ is    $2107$