Question

What is the maximum value of the sum of the AP 50, 48, 46, 44, ... ? [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

For maximum value of the given sequence to n terms, the nth term should be either zero or the smallest positive number of the sequence.

$i.e.,50+(n-1)(-2)=0[n^{th}termofanAP=a+(n-1\left)d\right]$

$\Rightarrow 50-2n+2=0$

$\Rightarrow n=26$

$\therefore S_{26}=\frac{26}{2}(50+0)=26\times 25=650$