Question

find the sum of all natural number less than 500 that are divisible by 7​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{All natural numbers less than 500}$

$\underline{\textbf{To find:}}$

$\textsf{The sum of all natural numbers less than 500}$

$\textsf{and divisible by 7}$

$\underline{\textbf{Solution:}}$

$\textsf{Natural numbers less than 500 and divisible by 7 are}$

$\mathsf{7,14,21,28.\;.\;.\;.\;.\;.497}$

$\textsf{Required sum}$

$\mathsf{=7+14+21+\;.\;.\;.\;.+497}$

$\mathsf{=7(1+2+3+\;.\;.\;.\;.+71)}$

$\mathsf{=7\left(\dfrac{n(n+1)}{2}\right)}$

$\mathsf{=7\left(\dfrac{71(71+1)}{2}\right)}$

$\mathsf{=7\left(\dfrac{71{\times}72}{2}\right)}$

$\mathsf{=7{\times}71{\times}36}$

$\mathsf{=497{\times}36}$

$\mathsf{=17892}$

$\therefore\boxed{\mathsf{Required\;sum=17892}}$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{7cm} \\\underline{\textbf{Sum of first n natural numbers:}}\\\\\mathsf{1+2+3+\;.\;.\;.\;.\;.+n=\dfrac{n(n+1)}{2}}\\ \end{minipage}}$