First slide

Arithmetic progression

Question

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

Moderate

A

310
B

300
C

320
D

318

Solution

nth term of the series =20+(n-1)(-2/3)
For the sum to be maximum, we must have nth term greater then or equal to 0.
$\begin{array}{l} \Rightarrow 20 + (n - 1) (- 2 / 3) \geq 0 \\ \Rightarrow n \leq 31 \\ ∴ the sum of the 31 terms is maximum = \frac{31}{2} (40 + 30 (- 2 / 3)) = 310 . \end{array}$

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