Question

find the sum of all natural number which are less than 500and also which is multiply of 7​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{We have to find the sum of all natural numbers less than 500 that are}\\\text{multiples of 7}$

       $\text{We can covert this into an Arithmetic Progression (AP)}$

$\implies \text{First term}(a) = 7$

       $\text{Common difference}(d)= 7$

       $\text{Last term}(l) = 497$

       $\text{Number of terms}(n) = \dfrac{497}{7} = 71$

       $\text{We know that, sum of }n \text{ terms in an AP}(s_n) = \dfrac{n}{2}(a + l)$

$\implies \text{Sum of 71 terms} = \dfrac{71}{2}(7 + 497)$

$\implies \text{Sum of 71 terms} = \dfrac{71}{2}(504)$

$\implies \text{Sum of 71 terms} = 71(252)$

$\implies \text{Sum of 71 terms} = 17892$

 $\therefore \text{ }\text{ }\boxed{\text{The sum of all multiples of 7 less than 500}=17892}$