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

ConceptArithmetic Progression - Finding Sum of Their First ‘N’ Terms.

#### 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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#### APPEARS IN

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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