Question

A manufacturer of TV set produced $720$ sets in fourth year and $1080$ sets in the sixth year. Assuming that the production increases uniformly by a fixed number every year, then find total production in first 9 years.

Answer 1

Production increases by a fixed number every year . So the production in consecutive years will form an AP

Let production in first year be $a$ and it increases by $d$ every year

$a_4=720a+(4-1)d=720\Rightarrow a+3d=\mathrm{720.......}\left(i\right)a_6=1080a+(6-1)d=1080\Rightarrow a+5d=\mathrm{1080......}\left(ii\right)$

solving first and $\left(ii\right)$ we get

$a=180,d=180$

Production in first nine years is the sum of first nine terms

$S=\frac{9}{2}\left\{2\right(180)+(9-1\left)180\right\}S=\frac{9}{2}\times 1800=8100$