SOLUTION: If you save 10$ one month, 12$ the next month, 14$ the next month, and so on, how long will you take to save a total of 400$? How would you make this into a formula?

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Question 346655: If you save 10$ one month, 12$ the next month, 14$ the next month, and so on, how long will you take to save a total of 400$?
How would you make this into a formula?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
you are looking for summing an arithmetic series
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the sequence is 10,12,14,..... such that is sum =400
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a%5Bi%5D=a%5B0%5D%2B%28i-1%29%2Adelta where delta is the difference between to consecutive sequence numbers, in this case a%5B0%5D=10 and delta=2
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a%5Bi%5D=10%2B%28i-1%29%2A2=8%2B2i
sum%28a%5Bi%5D%29from 1 to n =sum%28%288%2B2i%29%29= sum%288%29%2B2%2Asum%28i%29=8n+%2B+2%2A%28n%2A%28n%2B1%29%2F2%29=8n%2Bn%2A%28n%2B1%29=8n%2Bn%5E2%2Bn=n%5E2%2B9n
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since we want to know when this sum=400
400=n%5E2%2B9n--> 0=n%5E2%2B9n-400
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solve for n using quadratic formula
+n=%28-9%2B-sqrt%2881-4%2A%28-400%29%29%29%2F2
n=-25 or n=16, since we want the number of months, we take the positive answer
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highlight%28n=16+months%29