Just AP 3
Let be a finite arithmetic progression such that the first term is a negative number and for , the term of this progression is equal to 0. Find the sum of the first terms of this progression.
The answer is 0.
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The first term is a negative number provea that the common difference is not equal to 0.
Now, we see that the number of terms are odd (2k - 1). And we are also given that the k th term (which is the middle term) is 0. So, there are (k-2) terms on either side of 0 with the the same common difference which means that the terms equidistant from 0 are equal in magnitude and opposite in sign. So, adding them, they cancel out each other and gives the sum 0 .