Question

In an A.P of $99$ terms, the sum of all odd numbered terms is $2550$. Then find the sum of all the $99$ terms of the $A.P$.

Answer 1

We know

Sum of $n$ terms in $AP$

$S_n=\frac{n}{2}(T_1+T_n)$
Given that:
$\frac{50}{2}(T_1+T_{99})=2550$

$T_1+T_{99}=102$
Now, sum of all the $99$ terms-
$\frac{99}{2}(T_1+T_{99})$

$\Rightarrow \frac{99}{2}\times 102$

$\Rightarrow 5049.$

Hence, this is the required answer.