find the sum of all natural number between 200 and 400 which are divisible by 7
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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 = 399 = a + (n –1) d
⇒ 399 = 203 + (n –1) 7
⇒ 7 (n –1) = 196
⇒ n –1 = 28
⇒ n = 29
s29=29/2 (203+399)
= 29/2(602)
= (29)(301)
=8729
Thus, the required sum is 8729.
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