Question

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

(i) the production in the 1st year (ii) the production in the 10th year (iii) the total production in first 7 years

Answer 1

(i) Since the production increases uniformly by a fixed number every year, the number of TV sets manufactured in 1st, 2nd, 3rd, . . ., years will form an AP.

Let us denote the number of TV sets manufactured in the nth year by an.

Then, a3 = 600 and a7 = 700

or, a + 2d = 600

and a + 6d = 700

Solving these equations, we get d = 25 and a = 550.

Therefore, production of TV sets in the first year is 550.

(ii) Now a10 = a + 9d = 550 + 9 × 25 = 775

So, production of TV sets in the 10th year is 775.

Thus, the total production of TV sets in the first 7 years is 4375.