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Question
Find the sum of all multiples of 7 lying between 300 and 700.
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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) × 7
`=>` 392 = (n – 1) × 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 × 497
= 28329
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