SOLUTION: Find the amount of terms in arithmetic sequence with given terms. the first term is 1. The common difference is 1. and the sum is 8515

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Question 965727: Find the amount of terms in arithmetic sequence with given terms. the first term is 1. The common difference is 1. and the sum is 8515
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
The series is 1,2,3,................
Sum=8515
Sum=n(n+1)/2 where n is the number of terms
n(n+1)/2=8515
n(n+1)=17030
n^2+n-17030=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-17030+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A-17030=68121.

Discriminant d=68121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+68121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+68121+%29%29%2F2%5C1+=+130
x%5B2%5D+=+%28-%281%29-sqrt%28+68121+%29%29%2F2%5C1+=+-131

Quadratic expression 1x%5E2%2B1x%2B-17030 can be factored:
1x%5E2%2B1x%2B-17030+=+1%28x-130%29%2A%28x--131%29
Again, the answer is: 130, -131. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-17030+%29

The number of terms is 130.