Question

The sum of natural number between 400 to 600 divisible by 11

Answer 1

The numbers lying between 200 and 400, which are divisible by 7, are

203, 210, 217, ­­­­­­­­… 399

∴First term, a = 203

Last term, l = 399

Common difference, d = 7

Let the number of terms of the A.P. be n.

∴ an = 399 = a + (n –1) d

⇒ 399 = 203 + (n –1) 7

⇒ 7 (n –1) = 196

⇒ n –1 = 28

⇒ n = 29

therefore space S subscript 29 space equals space 29 over 2 space open parentheses 203 space plus space 399 close parentheses

space space space space space space space space space space space space space equals space 29 over 2 space open parentheses 602 close parentheses

space space space space space space space space space space space space space equals space open parentheses 29 close parentheses open parentheses 301 close parentheses

space space space space space space space space space space space space space equals space 8729

Thus, the required sum is 8729.