While deriving the formula for the sum of the first terms of an arithmetic…

MATHEMATICS · Single correct · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

While deriving the formula for the sum of the first nn terms of an arithmetic progression by pairing the first and last terms, which statement is true when nn is odd? (a) There are n+12\dfrac{n+1}{2} complete pairs because the middle term is counted as a pair with itself. (b) There are n−12\dfrac{n-1}{2} complete pairs and one unpaired middle term. (c) All nn terms can be completely paired, giving n2\dfrac{n}{2} pairs even when nn is odd. (d) The pairing method works only when nn is even; it cannot be applied when nn is odd.

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