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Question

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

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Solution

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=a+(n1)d = 399

⇒ 399 = 203 + (n –1) 7

⇒ 7 (n –1) = 196

⇒ n –1 = 28

⇒ n = 29

Sn=n2[a+L]

S29=292[203+399]

=292×602=8729

Thus, the required sum is 8729.


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