Find the sum of the series

To Find: The sum of the given series.

The nth term of an AP series is given by

$t_{n}=a+(n-1) d$

$\Rightarrow 191=2+(n-1) 3$

$\Rightarrow 3(n-1)=189$

$\Rightarrow n-1=63$

$\Rightarrow n=64$

Therefore,

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$S_{n}=\frac{64}{2}[4+63 \times 3]$

= 32 × 193 = 6176

The sum of the series is 6176.