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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
Natural numbers between 200 and 400 which are divisible by 7 are 203, 210 ,.... 399.
This is an AP with a = 203, d = 7 and l = 399.
Suppose there are n terms in the AP. Then,
an = 399
⇒ 203 + (n-1) × 7 = 399 [an = a+ (n-1) d]
⇒ 7n + 196 =399
⇒ 7n = 399-196 =203
⇒ n = 29
`∴ "Required sum " = 29/2 (203+399) [ s_n = n/2 (a+l)]`
`= 29/2 xx 602`
= 8729
Hence, the required sum is 8729.
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