SOLUTION: find the minimum number of AP 1,8,15............. such that the sum is greater than 1000

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Question 946119: find the minimum number of AP 1,8,15............. such that the sum is greater than 1000
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D=1%2B7%28n-1%29
S%5Bn%5D=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29%0D%0A%7B%7B%7BS%5Bn%5D%3E1000
%28n%2F2%29%281%2B1%2B7%28n-1%29%29%3E1000
n%282%2B7n-7%29%3E2000
n%287n-5%29%3E2000
7n%5E2-5n-2000%3E0
Let's find the solution when it does equal zero by completing the square.
7n%5E2-5n-2000=0
7%28n%5E2-%285%2F7%29n%29-2000=0
7%28n%5E2-%285%2F7%29n%2B%285%2F14%29%5E2%29=2000%2B7%285%2F14%29%5E2
7%28n-5%2F14%29%5E2=2000%2B175%2F196
7%28n-5%2F14%29%5E2=392175%2F196
%28n-5%2F14%29%5E2=56025%2F196
n-5%2F14=0+%2B-+sqrt%2856025%29%2F14
n=5%2F14+%2B-+%2815sqrt%28249%29%29%2F14
We're only interested in positive values,
n=5%2F14%2B%2815%2F14%29sqrt%28249%29}
n=17.26
Since we only use integral values, choose the next one up.
n=18