SOLUTION: Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n. Part (b): Find all pairs of positive integers (a,n) such that n greater than 2 and a + (a +

Question 1064993: Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n.
Part (b): Find all pairs of positive integers (a,n) such that n greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100. I don't understand how to do it and I've read many lessons.

Answer by ikleyn(52905)   (Show Source): You can put this solution on YOUR website!
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Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n.
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This is the sum of the first "n" terms of the arithmetic progression with the first term "a" and the common difference 1.

Everybody who studied arithmetic progressions knows the answer.

See the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
in this site.

You don't need to read many lessons. Read these two lessons only.

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