For an arithmetic progression with first term and common difference

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

Problem

For an arithmetic progression with first term aa and common difference dd, the sum written forward is added term-wise to the same sum written backward. Which of the following represents 2Sn2S_n obtained after this addition? (a) n[2a+(n+1)d]n\left[2a+(n+1)d\right] (b) n[2a+(n−1)d]n\left[2a+(n-1)d\right] (c) n2[2a+(n−1)d]\dfrac{n}{2}\left[2a+(n-1)d\right] (d) n[a+(n−1)d]n\left[a+(n-1)d\right]

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