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Topic: **How to write a mathematical equation****Question:**
How do I find the sum of the following numbers:
3+7+11+15+19+. . . . +403
I know I can simply add them all up number by number, but I know there's a formula to use. That's what I'm wondering if anyone knows.
Also, the numbers continue, the ". . . " is simply so I don't have to write all the numbers out. So it's not "something you learn in 1st grade." Thanks tho.

May 19, 2019 / By Kathie

First, you have to identify the pattern in these numbers. The pattern: 3 = 4*(0)+3 7 = 4*(1)+3 11 = 4*(2)+3 15 = 4*(3)+3 ... 403 = 4*(100)+3 In this case, you are summing up (4*n+3), where n = 0,1,...100. I believe that you are learning the summation notation. The mathematical equation is: summation of (4*n+3) from 0 to 100 = 3 + summation of (4*n+3) from 1 to 100 = 3 + summation of (4*n) from 1 to 100 + 3 *(100) <-- adding 3 for 100 times = 3+ 4 * (summation of n from 1 to 100) + 3*(100) <-- let's say if you have 4a+4b, you can write it as 4(a+b). there is a theorem that says, summation of n from 1 to k = (k*(k+1))/2, so your equation will become = 3+ 4 * ( ((100)*(100+1)/2) ) + 3*(100) = 20503 It's hard to explain by typing in a computer, but I hope it helps you understand!

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Did you like the answer? We found more questions related to the topic: **How to write a mathematical equation**

for the mean: add all your numbers and devide by 7 for the median: arrange them all in order according to size 5,8,9,9,10,13,16 and pick the one thats in the middle..in this case, 9. for the mode: the one that appears the most often

The mean (or average) is the sum of the numbers divided by 7 (the number of values) The median is the middle value when the numbers are ordered (9 in this case) The mode is the most prevalent value (9 in this case) SS is the sum or the squares -- square each number and add the squares SD is the standard deviation --multiply the SS by n, subtract from this the sum of the numbers squared; divide this by n(n-1) (42 in this case) if this is a sample from a population. Then take the square root of the whole thing. If it is NOT a sample from a population, then divide by n and take the square root of the whole thing.

Long winded method: work out all the numbers [each number adds 4] then add them altogether. There probably is an easier method but I can't think of it.

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Don't worry.Ask yourself, How many quarts are in a gallon? 4, so your expression would need to be 4 x g. Remember: a variable expression is an expression using a variable to replace the state or value of a number. Hope I helped.

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