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Find the Sum of All Multiples of 7 Between 300 and 700. - ICSE Class 10 - Mathematics

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Question

Find the sum of all multiples of 7 between 300 and 700.

Solution

Numbers between 300 and 700 which are multiples of 7 are as follows:

301, 308, 315, 322, ....., 693

Clearly, this forms an A.P with first term a = 301, common difference d = 7 and last term l = 693

l = a + (n - 1)d

`=> 693 = 301 + (n - 1) xx 7`

`=> 392 = (n - 1) xx 7`

=> n - 1 = 56

=> n = 57

Sum of first n terms = `S = n/2 [a + l]`

=> Required sum = `57/2 [301 + 693]`

`= 57/2 xx 994`

`= 57 xx 497`

= 28329

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Solution Find the Sum of All Multiples of 7 Between 300 and 700. Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms..
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