Question

What is the maximum sum of the terms in the arithmetic progression $25,24\frac{1}{2},24,........?$

• A. $637\frac{1}{2}$
• B. $625$
• C. $662\frac{1}{2}$
• D. $650$

Answer 1

The correct option is A

$637\frac{1}{2}$

The maximum sum would occur when we take the sum of all the positive terms of the series. The series 25, 24.5, 24, 23.5, 23,...1, 0.5, 0 has 51 terms. The sum of the series would be given by:
$n\times average=51\times 12.5=637.5$