First slide

Arithmetic progression

Question

The sum of the numbers between 200 and 400 that are divisible by 7 is

Moderate

A

8729
B

7511
C

6328
D

5712

Solution

Required numbers are
$\begin{array}{l} 203, 210, \dots, 399 \\ Now, 399 = 203 + 7 (n - 1) \\ \Rightarrow 57 = 29 + (n - 1) \Rightarrow n = 29 \end{array}$
Thus required sum is
$= \frac{29}{2} [203 + 399] = 8729$

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