5 + 10+15+20=50 ans
The sum of all multiples of 3 below 500 is the sum of 3 + 6 + ... + 498 = 41583The sum of all multiples of 5 below 500 is the sum of 5 + 10 + ... + 495 = 24750Depending upon the interpretation of "of 3 and 5", the answer is one of:The sum of all multiples of both 3 and 5 below 500 is the sum of 15 + 30 + ... + 495 = 8415The sum of all multiples of 3 below 500 and all multiples of 5 below 500 is 41583 + 24750 = 66333Since the multiples of both 3 and 5 (that is 15, 30, ...) have been counted twice - once in the multiples of 3 and once in the multiples of 5 - the sum of all multiples of 3 or 5 or both below 500 is 41583 + 24750 - 8415 = 57918I have emphasised the word below with regard to 500 since 500 is a multiple of 5, but 500 is not below (less than) itself, that is the multiples are of the numbers 1, 2, 3, ..., 499. If the question was intended to mean less than or equal to 500, add an extra 500 to the multiples of 5 above, making the sum of the multiples of 5 be 25250 and the final sums (1) 8415, (2) 66833, (3) 58418.
Well, you could add them one by one, or write a small computer program to do that, but here is a shortcut:Use the formula for an arithmetic series, to find the sum of all the multiples of 3 (3, 6, ... 999).Similarly for all the multiples of 5 (5, 10, ... 995).Add it all up.Multiples of 15 will be counted twice in his calculation, so you'll have to calculate the sum of all the multiples of 15, and subtract it from the above.Well, you could add them one by one, or write a small computer program to do that, but here is a shortcut:Use the formula for an arithmetic series, to find the sum of all the multiples of 3 (3, 6, ... 999).Similarly for all the multiples of 5 (5, 10, ... 995).Add it all up.Multiples of 15 will be counted twice in his calculation, so you'll have to calculate the sum of all the multiples of 15, and subtract it from the above.Well, you could add them one by one, or write a small computer program to do that, but here is a shortcut:Use the formula for an arithmetic series, to find the sum of all the multiples of 3 (3, 6, ... 999).Similarly for all the multiples of 5 (5, 10, ... 995).Add it all up.Multiples of 15 will be counted twice in his calculation, so you'll have to calculate the sum of all the multiples of 15, and subtract it from the above.Well, you could add them one by one, or write a small computer program to do that, but here is a shortcut:Use the formula for an arithmetic series, to find the sum of all the multiples of 3 (3, 6, ... 999).Similarly for all the multiples of 5 (5, 10, ... 995).Add it all up.Multiples of 15 will be counted twice in his calculation, so you'll have to calculate the sum of all the multiples of 15, and subtract it from the above.
Sum of first 25 multiples of 44+8+12....100taking 4 common4(1+2+3+4....+25) = 4*325 =1300
The first ten multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30.
The sum of the first 10 multiples of 3 is 165.
5 + 10+15+20=50 ans
975
Since 3 is a factor of 15, the first three common multiples of 3 and 15 are 15, 30, and 45.
The first 5 multiples of 3 are as follows: 3, 6, 9, 12, 15
Created in a spreadsheet, the answer is: 375750
The sum of all multiples of 3 below 500 is the sum of 3 + 6 + ... + 498 = 41583The sum of all multiples of 5 below 500 is the sum of 5 + 10 + ... + 495 = 24750Depending upon the interpretation of "of 3 and 5", the answer is one of:The sum of all multiples of both 3 and 5 below 500 is the sum of 15 + 30 + ... + 495 = 8415The sum of all multiples of 3 below 500 and all multiples of 5 below 500 is 41583 + 24750 = 66333Since the multiples of both 3 and 5 (that is 15, 30, ...) have been counted twice - once in the multiples of 3 and once in the multiples of 5 - the sum of all multiples of 3 or 5 or both below 500 is 41583 + 24750 - 8415 = 57918I have emphasised the word below with regard to 500 since 500 is a multiple of 5, but 500 is not below (less than) itself, that is the multiples are of the numbers 1, 2, 3, ..., 499. If the question was intended to mean less than or equal to 500, add an extra 500 to the multiples of 5 above, making the sum of the multiples of 5 be 25250 and the final sums (1) 8415, (2) 66833, (3) 58418.
4 + 8 + 12 = 24
10+20+30 = 60
Sum_ap = ½ × number_of_terms × (first_term + last_term) For the first 88 multiples of three: number_of_terms = 88 first_term = 1 × 3 = 3 last_term = 88 × 3 = 264 → Sum = ½ × 88 × (3 + 264) = 44 × 267 = 11748
15, 30, 45
The first six multiples of 3 are 3, 6, 9, 12, 15, and 18.