Question

samt le 16 A manufacturer of TV sets produced 600 sets in the third year and sed in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : a) the production in the 1st year (ii) the production in the 10th ye in the total production in first 7 years​

Answer 1

Let 'a' be the first term and 'd' be the common difference of the A.P formed

$\small \bold{a_3=a+2d=600-----(i)}$

$\small \bold{And \: a_7=a+6d=700----(ii)}$

Solving equation (i) and (ii)

a=550 and d=5

(i) Production in the first year is 550 TV sets.

(ii) Production in the 10th year

$\bold{= a_{10} =a+9d}$

=550+9(25)

=550+225

=775

(iii) Total production in 7 years =

$\bold{S_7 = \frac{7}{2} [2(550) + (7 - 1)25]}$

=4375.

Thus, the total production in 7 years if of 7375 TV sets