Question

A TV manufacturer has produced $1000$ TV's in the seventh year and $1450$ TV's in the tenth year.Assuming that the production increases uniformly by a fixed number every year, find the number of TV's produced in the first year and the fifteenth year.

Answer 1

Given that: $T_7=1000\&T_{10}=1450$

where $T_7\&T_{10}$ represents the number of units produced in the seventh year and number of units produced in $10th$ year respectively.

Let's say the first year production was ${}^{\prime }{a}^{\prime }$ units and the production increases by ${}^{\prime }{d}^{\prime }$ every year then

$T_7=a+6d,T_{10}=a+9d\therefore a+6d=1000-\left(1\right)a+9d=1450-\left(2\right)$

Subtracting $\left(1\right)$ & $\left(2\right)$, we get

$3d=450d=150\therefore a=100\therefore T_{15}=a+14d=100+(14\times 150)=2200$

So in the first year $100$ TV were produced.

and in $15th$ year we will have $2200$ TV.