Question

5. Find the sum of all natural numbers between 200 and 1000 exactly divisible by 6.
Ans. S = 79800​

Answer 1

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

$\textsf{The sum of all natural numbers}$

$\textsf{200 and 1000 divisible by 6}$

$\underline{\textsf{Solution:}}$

$\textsf{The numbers divisible by 6 are}$

$\mathsf{204,210,..........996}$

$\textsf{Clearly, they form an A.P}$

$\textsf{Here, a=204, d=6, l=996}$

$\textsf{Number of terms in the A.P}$

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

$\mathsf{n=\dfrac{996-204}{6}+1}$

$\mathsf{n=\dfrac{792}{6}+1}$

$\mathsf{n=132+1}$

$\mathsf{n=133}$

$\textsf{Required sum}$

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

$\mathsf{S_n=\dfrac{133}{2}[204+996]}$

$\mathsf{S_n=\dfrac{133}{2}[1200]}$

$\mathsf{S_n=133{\times}600}$

$\mathsf{S_n=79800}$

$\underline{\textsf{Answer:}}$

$\textsf{The sum of all natural numbers}$

$\textsf{200 and 1000 divisible by 6 is 79800}$

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