Sum of Multiples of 7 Between 1 and 500 | AP Sums Made Easy

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[00:00:00]This question can save or lose you marks in exams.

[00:00:04]Find the sum of all multiples of seven between 1 and 500.

[00:00:09]Let's solve step by step. Multiples of seven form an arithmetic sequence.

[00:00:15]Now, use the formula. Last term is equal first term plus n minus 1 times the common difference d.

[00:00:22]So, we write 497 equals 7 plus n minus 1 times 7. Which gives us 497 equals 7n.

[00:00:31]So, n equals 71.

[00:00:34]Now, use the sum formula. So, we get s equals 71 divided by 2 times 7 plus 497.

[00:00:41]Which gives us s equals 71 times 252.

[00:00:45]So, s equals 17,892.

[00:00:49]So, the sum of all multiples of seven between 1 and 500 is 17,892.

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