The production of TV sets in a factory increases uniformly by a fixed number every year . It produced 16000 sets in 6th year and 2

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.​

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  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

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