The production of TV in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year and 11300 in 9th year. Then the production in the 6 years is

Since, production of TV in 6^th year $=8000$

$\Rightarrow a_6=800\Rightarrow a+5d=8000\cdots \cdots \cdots \left(1\right)$

Also production of TV in 9^th year $=11300$

$a_9=11300$  or $a+8d=11300\cdots \cdots \cdots \left(2\right)$

Subtracting (1) from (2), we get

$3d=3300\Rightarrow d=1100$

From (1) $a=2500$

$\therefore$ Production in 6 years, i.e., $S_6=\frac{6}{2}\left[2\left(2500\right)+\left(6-1\right)\left(1100\right)\right]=31500$