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

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

are as follows: -

203, 210, 217, … 399

Since the common difference between the consecutive terms is constant. Thus, the above sequence is an A.P.

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

We know that -

Sum of n terms of an A.P(Sn) = (n/2)[a + l]

S29 = (29/2)[203 + 399]

= (29/2)

= 29 × 301

= 8729

Thus, the required sum is 8729.

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