Find the sum of all numbers between 200 and 4 | vedclass

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Question

(A) The numbers between $200$ and $400$ that are divisible by $7$ form an arithmetic progression: $203, 210, 217, \dots, 399.$Here,the first term $a =

Vedclass · Accepted Answer

$8729$

Vedclass · Answer

(A) The numbers between $200$ and $400$ that are divisible by $7$ form an arithmetic progression: $203, 210, 217, \dots, 399.$Here,the first term $a = 203$ and the last term $l = 399.$The common difference $d = 7.$Using the formula for the $n^{th}$ term of an $A.P.$,$a_n = a + (n - 1)d:$$399 = 203 + (n - 1)7$$196 = (n - 1)7$$n - 1 = 28$$n = 29.$The sum of $n$ terms is given by $S_n = \frac{n}{2}(a + l):$$S_{29} = \frac{29}{2}(203 + 399)$$S_{29} = \frac{29}{2}(602)$$S_{29} = 29 	imes 301 = 8729.$Thus,the required sum is $8729.$

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

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