Question

The production of TV sets in a factory increases uniformly by a fixed number every year . It produced 16000 sets in 6th year and 22600 in 9th year.

1. Find the production in first year.
2.Find the production in 8th year.
3. Find the production during first 3 years.
4. In which year, the production is Rs. 29,200.​

Answer 1

Step-by-step explanation:

Solution :

Let the production during first year be a and let d be the increase in production every year. Then,

T6=16000⇒a+5d=16000…(i)

andT9=22600⇒a+8d=22600...(ii)

On subtracting (i) from (ii), we get

3d=6600⇒d=2200

Putting d = 2200 in (i), we get

a+5×2200=16000⇒a+11000=16000

⇒a=16000-11000=5000

Thus, a = 5000 and d = 2200.

(i) Production during first year, a = 5000

(ii) Production during 8th year is given by

T8=(a+7d)=(5000+7×2200)=(5000+15400)=20400.

(iii) Production during first 6 years is given by

S6=

6

2

{2a+5d}=3(2×5000+5×2200)

=3(10000+11000)=63000