Sum of A.S

[martianxx]

I had a question in a recent exam that asked you to prove the formula to calculate the sum of an A.S. I only got 2/11 on it so i was wondering if someone could tell me it. I have searched the internet for one but all seem to be a bit rubbish and i think i can get better results here

[Country Boy]

The nice thing about arithmetic sequences is that the "average" of all the numbers in the sequence is just the average of the first and last numbers. That is, if the sequence {a1, a2, ..., an} is an arithmetic sequence, then

(a1+ a2+ ... + an)/n= (a1+ an)/2. And so the sum, a1+ a2+ ... an is just that average (a1+a2)/2 times n.