Find the sum of all numbers between 200 and 400 which are divisible by 7.

Answer

N/a

Explanation

Numbers between 200 and 400, divisible by 7
`= 203, 210, 217, …, 399`
Here, a = 203, common difference d = 210 - 203 = 7
Let total numbers be n, then `T_(n) = 399`
`rArr` a + (n - 1)d = 399
`rArr` 203 + (n - 1)7 = 399
`rArr` (n - 1)7 = 399 - 203 = 196
`rArr` `(n-1) = (196)/(7) = 28 " " rArr " " n = 1 + 28 = 29`
`because` Sum of n numbers `= (n)/(2)[2a + (n -1)d]`
`therefore` `S_(29) = (29)/(2)[2 xx 203 + (29 - 1)7]`
`= (29)/(2) [406 + 196]`
`= (29)/(2) xx 602 = 29 xx 301 = 8729`