Question

If the sum of 99 terms of AP is 198, then what is the value of the 50th term?

Answer 1

Let the first term of the AP be $a$, and the common difference be $d$.
Given: Sum of 99 terms is 198
$S_{99}=198\Rightarrow \frac{99}{2}[2a+(99-1\left)d\right]=198[S_n=\frac{n}{2}[2a+(n-1)d]$
$\Rightarrow 2a+98d=\frac{198\times 2}{99}=4$
$\Rightarrow a+49d=2$
$\Rightarrow a+(50-1)d=2$
$\Rightarrow a_{50}=2[n^{th}termofanAP=a+(n-1\left)d\right]$
$\therefore$ The 50th term is 2.