First slide

Arithmetic progression

Question

$The maximum sum of the series 20 + 19 \frac{1}{3} + 18 \frac{2}{3} + \dots \dots is$

Moderate

A

310
B

300
C

320
D

330

Solution

$nth term of the series is 20 + (n - 1) (- 2 / 3)$
$For the sum to be maximum nth term \geq 0 \Rightarrow 20 + (n - 1) (- \frac{2}{3}) \geq 0$
Thus, the sum of 31 terms is maximum and is $\frac{31}{2} [40 + 30 \times (- \frac{2}{3})] = 310$

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