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tangibleLime
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Homework Statement
The sequence a0 -> n is defined by ai = b+i*c. Prove by induction on n that the sum of the terms in the sequence is (n+1)(a0 + an)/2.
Homework Equations
The Attempt at a Solution
I defined predicate P(n) as (n+1)(a0+an)/2.
My goal is P(n+1), which is (n+2)(a0+an+1)/2. I believe I may have made a mistake here. For some reason I think it might be (n+2)(a0+an+an+1)/2, but I'm not sure.
So to prove P(n+1), I take P(n) and add the new term to it, (an+1).
P(n) + an+1
= ((n+1)(a0+an)/2) + (an+1)
= ((n+1)(a0+an) + 2(an+1))/2
Obviously what I got here is not visually equal to P(n+1), but maybe I'm missing something simplifying-wise? Or did I make a mistake somewhere?
And yes, I know I also have to test the base case, which I can do easily.
Any help would be appreciated!