Question

In an arithmetic progression containing $99$ terms, the sum of all the odd numbered terms is $2550.$ If the sum of all the $99$ terms of the arithmetic progression is $k$ , then $\frac{k}{100}$ is equal to

Answer 1

Let the terms of AP be $a,a+d,a+2d,\ldots ..,a+98d$
For sum of all odd numbered terms $A=a,D=2d,N=50.$
i.e. $\frac{50}{2}(2 a+49(2 d))=2550$
$\Rightarrow 2a+98d=102$
Sum of all $99$ terms is,
$\frac{99}{2}\left(2 a + 98 d\right)=\frac{99}{2}\times 102=99\times 51$
$\Rightarrow k=5049\Rightarrow \frac{k}{100}=50.49$