A sports day committee arranges plastic chairs for spectators in 10 successive rows

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

A sports day committee arranges plastic chairs for spectators in 10 successive rows. The first row contains 20 chairs and each successive row contains the same number of additional chairs so that the arrangement forms an arithmetic progression. (i) Determine the common difference between successive rows if the last row contains 38 chairs. (ii) Calculate the total number of chairs used in all 10 rows. (iii) The committee later decides to increase the seating capacity to at least 500 chairs by adding more rows at the end of the same pattern (keeping the common difference found in part (i)). Find the minimum number of additional rows that must be added and the number of chairs in the new last row.

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