# A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year.

Question:

A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find

(i) the production in the first year

(ii) the total product in 7 years and

(iii) the product in the 10th year.

Solution:

Let $a_{n}$ denote the production of radio sets in the $n$th year.

Here, $a_{3}=600, a_{7}=700$

We know:

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

$a_{3}=a+2 d$

$\Rightarrow 600=a+2 d \quad \ldots \ldots(1)$

And, $a_{7}=a+6 d$

$\Rightarrow 700=a+6 d \quad \ldots .(2)$

Solving 1">(1)and 2">(2)we get:

d = 25, a = 550

Hence, the production in the first year is 550 units.

(ii) Let $S_{n}$ denote the total production in $n$ years.

Total production in 7 years $=S_{7}$

$=\frac{7}{2}\{2 \times 550+(7-1) 25\}$

$=4375$ units

(iii) Production in the 10th year $=a_{10}$

$a_{10}=a+(10-1) d$

$=550+9(25)$

$=775$