SOLUTION: What is the last number in this sum? 1 + 3 + 5 + ... + ? = 10,000

Question 443549: What is the last number in this sum?
1 + 3 + 5 + ... + ? = 10,000
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let n=number of terms in the sum.
The first term (a[1]) is 1.
The last term (a[n]) must be 2n-1.
n/2(a[1]+a[n])=S Formula for the sum of an finite arithmetic sequence.
n/2(1+(2n-1))=10000
n(1+2n-1)=20000
n+2n^2-n=20000
2n^2=20000
n^2=10000
n=100
a[100]=2*100-1=199
.
Ed
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