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August 20th, 2008, 12:36 AM  #1 
Newbie Joined: May 2008 From: Melbourne Posts: 24 Thanks: 0  sequences and series: Arithmetic Sequences
Consider the sum of the first n integers. For what value of n will the sum first exceed 1000 ? And the formula to find the sum of n terms in an arithmetic sequence is Sn: n/2(2a+(n1)d) where a is the first term and d is the difference 
August 20th, 2008, 03:40 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958 
The problem should have specified positive integers. The sequence (of positive integers ? n) in the problem then starts at 1 and has a common difference of 1, so the formula you gave, with a = d = 1, gives the sum of the integers 1, 2, . . . , n as n(n + 1)/2. Hence the integer value you have to find will be a little greater than the square root of 2000.


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