What is the sum of multiples of seven between 1 and 100
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Answer:
How do I find the sum of all the multiples of 7 that are between 1 and 1,000?
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First, you need to understand that the sum of all multiples of 7 for n sequences is:
7+14+21+…+7n
Which is:
7(1+2+3+…+n)
Does (1+2+3+…+n) sound familiar to you? If you’re not familiar with that, remember that 1+n = 2+n-1 = 3+n-2 etc and count the number of pairs and multiply the number by the sum of one of the pair
Still don’t understand?
Take a look at the example below:
1+2+3+4+5+6+7+8+9
You will realise that 1+9=2+8=3+7 etc. Next, calculate the number of pairs of numbers with equal sums like the one above by taking the last number in the sum series and dividing it by 2. You will find out that 9/2 is 4.5. Round it down and you find out that there are 4 pairs of equal sums. Multiply it by 1+9, which is 10, and multiply it by 4. Then, find the median in the sequence by rounding up 4.5, which is 5. Consequently, add 40 to 5 and you get 45.
Alternatively, you can use this formula:
Where n is the number of sequences in the series.
Let’s get back to the question:
7+14+21+…+7n=7(1+2+3+…+n)
First, we need to find the number of sequences in the 7n sum series by dividing 1000 by 7 , which is 142.8. Then we round down 142 to get the number of sequences in the series. This is done to find the largest multiple of 7 less than 1000.
Next, use either of the methods mentioned above to find (1+2+3+…+n). I will use the formula in this example:
142(143)/2 = 10,153
Finally, multiply 10,153 by 7 to get 71,071. Voila!
Of course, there is always an option keying in 7+14+21+28 with a calculator
Step-by-step explanation:
2054
is the answer
for this questions