SOLUTION: Sabrina used a calculator and started adding the whole numbers in order: 1+2+3+4+5+ What is the last number she would add that would get the sum on her calculator over 1,000?

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Question 775148: Sabrina used a calculator and started adding the whole numbers in order:
1+2+3+4+5+
What is the last number she would add that would get the sum on her calculator over 1,000?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the formula is
1%2B2%2B3%2B4+...+n+=+n%28n%2B1%29%2F2
So we have an inequality because is given the sum on her calculator is over 1000.

n%28n%2B1%29%2F2+%3E+1000........ solve for n
n%28n%2B1%29+%3E+2000
n%5E2%2Bn+-2000%3E+0...solve as equation using quadratic formula

n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

n+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-2000%29+%29%29%2F%282%2A1%29+
n+=+%28-1+%2B-+sqrt%28+1%2B8000%29+%29%29%2F2+
n+=+%28-1+%2B-+sqrt%288001%29+%29%29%2F2+
n+=+%28-1+%2B-+89.45+%29%2F2+
solutions:
n+=+%28-1+%2B+89.45+%29%2F2+
n+=+88.45+%2F2+
n+=+44.225+..we need only positive solution, since the sum has to be > 1000
so, n has to be first greater number which is 45+